Find the volume of the right circular... -Maths 9th

Find the volume of the right circular... -Maths 9th
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Answer :

Volume of cone = 1/3 πr2h = 1/3 x 22/7 x (3.5)2 x 12 cm3 = 154 cm3.
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The volume of a right circular cone is 9856 cmcube. -Maths 9th

Description : The volume of a right circular cone is 9856 cmcube. -Maths 9th

Last Answer : Let the height of the cone be h cm. Radius of the base of the cone (r) = 28/2 cm = 14 cm Volume of the cone = 9856 cm3 ⇒ 1/3πr2h = 9856 ⇒ 1/3 x 22/7 x 14 x 14 x h = 9856 ⇒ h = 9856 x 7 x 3/ ... √196 + 2304) = √2500 ∴ l = 50 cm (iii) Curved surface area of cone = πrl = 22/7 x 14 x 50 = 2200 cm2

A right circular solid cone of maximum possible volume is cut off from a solid metallic right circular cylinder of volume V. -Maths 9th

Description : A right circular solid cone of maximum possible volume is cut off from a solid metallic right circular cylinder of volume V. -Maths 9th

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The magnitude of the volume of a closed right circular cylinder of unit height divided by the magnitude of the total surface area of the -Maths 9th

Description : The magnitude of the volume of a closed right circular cylinder of unit height divided by the magnitude of the total surface area of the -Maths 9th

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A right circular cylinder just encloses a sphere of radius r (see fig. 13.22). Find (i) surface area of the sphere, (ii) curved surface area of the cylinder -Maths 9th

Description : A right circular cylinder just encloses a sphere of radius r (see fig. 13.22). Find (i) surface area of the sphere, (ii) curved surface area of the cylinder -Maths 9th

Last Answer : Surface area of sphere = 4πr2, where r is the radius of sphere (ii) Height of cylinder, h = r+r =2r Radius of cylinder = r CSA of cylinder formula = 2πrh = 2πr(2r) (using value of h) = 4πr2 (iii) Ratio ... sphere)/CSA of Cylinder) = 4r2/4r2 = 1/1 Ratio of the areas obtained in (i) and (ii) is 1:1.

A joker’s cap is in the form of right circular cone of base radius 7 cm and height 24cm. Find the area of the sheet required to make 10 such caps. -Maths 9th

Description : A joker’s cap is in the form of right circular cone of base radius 7 cm and height 24cm. Find the area of the sheet required to make 10 such caps. -Maths 9th

Last Answer : Radius of conical cap, r = 7 cm Height of conical cap, h = 24cm Slant height, l2 = (r2+h2) = (72+242) = (49+576) = (625) Or l = 25 cm CSA of 1 conical cap = πrl = (22/7)×7×24 = 550 CSA of 10 caps = (10×550) cm2 = 5500 cm2 Therefore, the area of the sheet required to make 10 such caps is 5500 cm2.

The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. (Assume π =22/7 ) -Maths 9th

Description : The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. (Assume π =22/7 ) -Maths 9th

Last Answer : Height of cylinder, h = 14cm Let the diameter of the cylinder be d Curved surface area of cylinder = 88 cm2 We know that, formula to find Curved surface area of cylinder is 2πrh. So 2πrh =88 cm2 (r is the ... 88 cm2 2r = 2 cm d =2 cm Therefore, the diameter of the base of the cylinder is 2 cm.

What is the number of surfaces of a right circular cylinder ? -Maths 9th

Description : What is the number of surfaces of a right circular cylinder ? -Maths 9th

Last Answer : Number of surfaces of right circular cylinder are three.

The curved surface area of a right circular -Maths 9th

Description : The curved surface area of a right circular -Maths 9th

Last Answer : Curved surface area of cylinder = 2 πrh ⇒ 88 = 2 x 22/7 x r x 14 ⇒ r = 88 x 7/2 x 22 x 14 = 1 ∴ Diameter of the base of cylinder = 2r = 2 x 1 = 2 cm

A joker's cap is in the form of a right circular.... -Maths 9th

Description : A joker's cap is in the form of a right circular.... -Maths 9th

Last Answer : Radius of the base of the conical cap (r) = 7 cm Height of the conical cap (h) = 24 cm Let 'l' be the slant height of the conical cap. Then l = root under( √r2 + h2) = root under( √72 + 242) l = root ... cap = 22/7 x 7 x 25 cm2 = 550 cm2 ∴ Sheet required for 10 caps = 550 x 10 cm2 = 5500 cm2

In Fig., a right circular cylinder just encloses a sphere of radius r. Find -Maths 9th

Description : In Fig., a right circular cylinder just encloses a sphere of radius r. Find -Maths 9th

Last Answer : (i) Surface areas S1 of the sphere = 4 πr2 (ii) We have Radius of the cylinder = r Height of the cylinder = h = 2r ∴ Curved surface area S2 of the cylinder ... 2 πrh = 2 πr x 2r = 4 πr2 (iii) S1/S2 = 4 πr2/4 πr2 = 1/1 ∴ S1 : S2 = 1 : 1

A sphere and a right circular cylinder -Maths 9th

Description : A sphere and a right circular cylinder -Maths 9th

Last Answer : Let the radius of sphere and cylinder be r and h be the height of cylinder. Then according to the question. Volume of sphere = Volume of cylinder ⇒ 4/3πr3 = πr2h ⇒ r = 3/4.h Diameter of the cylinder = ... x 100 = h/2 x 1/h x 100 = 50% Thus, the diameter of the cylinder exceeds its height by 50%.

Define : Right circular cylinder. -Maths 9th

Description : Define : Right circular cylinder. -Maths 9th

Last Answer : A right circular cylinder is a cylinder that has a closed circular surface having two parallel bases on both the ends and whose elements are perpendicular to its base. It is also called a right ... circular surface is at a fixed distance from a straight line known as the axis of the cylinder.

Define : Right circular cone. -Maths 9th

Description : Define : Right circular cone. -Maths 9th

Last Answer : A right circular cone is a cone where the axis of the cone is the line meeting the vertex to the midpoint of the circular base. That is, the centre point of the circular base is joined with ... cone is a three-dimensional shape having a circular base and narrowing smoothly to a point above the base.

The area of the curved surface and the area of the base of a right circular cylinder are a square cm and b square cm respectively -Maths 9th

Description : The area of the curved surface and the area of the base of a right circular cylinder are a square cm and b square cm respectively -Maths 9th

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A right circular cylinder and a right circular cone have equal bases and equal volumes. But the lateral surface area of the right circular cone is -Maths 9th

Description : A right circular cylinder and a right circular cone have equal bases and equal volumes. But the lateral surface area of the right circular cone is -Maths 9th

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If S denotes the area of the curved surface of a right circular cone of height h end semi-vertical angle a, then S equals -Maths 9th

Description : If S denotes the area of the curved surface of a right circular cone of height h end semi-vertical angle a, then S equals -Maths 9th

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A sphere and a right circular cone of same radius have equal volumes. By what percentage does the height of the cone exceed its diameter ? -Maths 9th

Description : A sphere and a right circular cone of same radius have equal volumes. By what percentage does the height of the cone exceed its diameter ? -Maths 9th

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The diameter of a solid mettalic right circular cylinder is equal to its height. After culting out the largest possible solid sphere -Maths 9th

Description : The diameter of a solid mettalic right circular cylinder is equal to its height. After culting out the largest possible solid sphere -Maths 9th

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A solid right circular cylinder of radius 8 cm and height 2 cm is melted and cast into a right circular cone of height 3 times that of the cylinder. -Maths 9th

Description : A solid right circular cylinder of radius 8 cm and height 2 cm is melted and cast into a right circular cone of height 3 times that of the cylinder. -Maths 9th

Last Answer : Height of cone = 3 times height of cylinder = 3 3 = 9 cm Volume of cylinder = volume of cone r2 = 8 8 r = 8 cm l2 = h2 + r2 = (9)2 + (8)2 l = = 12 cm C.S.A (cone) = = 301.71 cm2

A child consumed an ice-cream of inverted right-circular conical shape from the top and left only 12.5% of the cone for her mother. -Maths 9th

Description : A child consumed an ice-cream of inverted right-circular conical shape from the top and left only 12.5% of the cone for her mother. -Maths 9th

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Prove that the volume of the largest right -Maths 9th

Description : Prove that the volume of the largest right -Maths 9th

Last Answer : Volume of the cone = 1/3πr2h = 1/3πr2 (2r) = 2/3πr3 = volume of the hemisphere

A right DABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. What is the volume of the solid so obtained ? -Maths 9th

Description : A right DABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. What is the volume of the solid so obtained ? -Maths 9th

Last Answer : From the figure it is clear that a cone is formed. Here, h = 12 cm, r = 5 cm Volume of cone = = 314 cm3

The base of a right prism is an equilateral triangle with a side 6 cm and its height is 18 cm. Find its volume, -Maths 9th

Description : The base of a right prism is an equilateral triangle with a side 6 cm and its height is 18 cm. Find its volume, -Maths 9th

Last Answer : Volume of a right prism = Area of base height. Since the base is an equilateral triangle of side 6 cm, Area of base = 3√434 x (side)2 = (3√4 62)(34 62)cm2 = 3√434 x 36 cm2 = 93-√93 cm2 ∴ Volume = (93-√93 x18) ... ) = (324 + 2 9√3 ) cm2 = (324 + 18√3 ) cm2 = (324 + 31.176) cm2 = 355.176 cm2.

The base in a right prism is an equilateral triangle of side 8 cm and the height of the prism is 10 cm. The volume of the prism is -Maths 9th

Description : The base in a right prism is an equilateral triangle of side 8 cm and the height of the prism is 10 cm. The volume of the prism is -Maths 9th

Last Answer : ⇒ Area of equilateral triangle =43 ( s i d e)2 =43 ( 8)2 =43 64 ... =3 3 2 . 5 5 4 cm3. =3 3 2 . 5 5 4 cc

What is the volume of a right prism standing on a triangular base of sides 5 cm, 5 cm and 8 cm whose lateral surface area is 828 cm^2 ? -Maths 9th

Description : What is the volume of a right prism standing on a triangular base of sides 5 cm, 5 cm and 8 cm whose lateral surface area is 828 cm^2 ? -Maths 9th

Last Answer : Lateral surface area of a prism = Perimeter of base Height ⇒ 840 = (5 + 5 + 8) Height ⇒ Height = 8401884018 = 46 cm. = Semi perimeter of the triangular base = 182182 = 9 cm ∴ Area of triangle = 9(9- ... 4 1 = 12 cm2 ∴ Required volume of prism = Area of base Height = (12 46) cm3 = 552cm3

If the base of right rectangular prism remains constant and the measures of the lateral edges are halved, then its volume will be reduced by : -Maths 9th

Description : If the base of right rectangular prism remains constant and the measures of the lateral edges are halved, then its volume will be reduced by : -Maths 9th

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The inner diameter of a circular well is 3.5m. It is 10m deep. Find (i) its inner curved surface area, (ii) the cost of plastering this curved surface at the rate of Rs. 40 per m2. -Maths 9th

Description : The inner diameter of a circular well is 3.5m. It is 10m deep. Find (i) its inner curved surface area, (ii) the cost of plastering this curved surface at the rate of Rs. 40 per m2. -Maths 9th

Last Answer : Inner radius of circular well, r = 3.5/2m = 1.75m Depth of circular well, say h = 10m (i) Inner curved surface area = 2πrh = (2 (22/7 ) 1.75 10) = 110 Therefore, the inner curved surface ... area = Rs (110 40) = Rs.4400 Therefore, the cost of plastering the curved surface of the well is Rs. 4400.

An amusement fair was organised in a circular park for the children of slum clusters. Free food was supplied to them at 4 stalls situated at A, B, C and D as shown in the given figure. -Maths 9th

Description : An amusement fair was organised in a circular park for the children of slum clusters. Free food was supplied to them at 4 stalls situated at A, B, C and D as shown in the given figure. -Maths 9th

Last Answer : (i) From figure , it is clear that angle between the lines joining stalls C,D and stalls C, B is ∠BCD . Given, ∠DBC = 60° and ∠BAC = 40° CD is a chord of circle. Here, ∠CBD and ... for society. (iii) Other social issues for which such compaigns are required, are old age home, orphanages, etc.

An amusement fair was organised in a circular park for the children of slum clusters. Free food was supplied to them at 4 stalls situated at A, B, C and D as shown in the given figure. -Maths 9th

Description : An amusement fair was organised in a circular park for the children of slum clusters. Free food was supplied to them at 4 stalls situated at A, B, C and D as shown in the given figure. -Maths 9th

Last Answer : (i) From figure , it is clear that angle between the lines joining stalls C,D and stalls C, B is ∠BCD . Given, ∠DBC = 60° and ∠BAC = 40° CD is a chord of circle. Here, ∠CBD and ... for society. (iii) Other social issues for which such compaigns are required, are old age home, orphanages, etc.

A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 8 m, find the cost of painting it on the outside at the rate of Rs. 10 per m -Maths 9th

Description : A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 8 m, find the cost of painting it on the outside at the rate of Rs. 10 per m -Maths 9th

Last Answer : Answer We have, r=0.7m, h=8m ∴ Total surface area = 2πr2+2πrh=2πr(r+h)=2×722​×0.7×8.7m2 Required cost = Rs. {2×722​×0.7×8.7×10}=Rs.382.80

The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find -Maths 9th

Description : The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find -Maths 9th

Last Answer : Radius of well = (r) = 3.5/2 m Depth of well = (h) = 10 m (i) Inner curved surface area of well = 2 πrh = 2 x 22/7 x 3.5/2 x 10 = 110 m2 (ii) Cost of plastering 1 m2 = ₹ 40 ∴ Cost of plastering 110 m2 = ₹110 X 40 = ₹4400

30 circular plates, each of radius 14 cm -Maths 9th

Description : 30 circular plates, each of radius 14 cm -Maths 9th

Last Answer : Height of the cylinder formed (h) = 30 x 3 = 90 cm Radius of the base of the cylinder formed (r) = 14 cm (i) Total surface area of the cylinder = 2 πr(r + h) = 2 x 22/7 x 14(14 + 90) = 2 x 22/7 x 14 x 104 = 9152 cm2 (ii) Volume of the cylinder formed = πr2h = 22//7 x 14 x 14 x 90 = 55440 cm3

A semi-circular sheet of metal of diameter 28 cm -Maths 9th

Description : A semi-circular sheet of metal of diameter 28 cm -Maths 9th

Last Answer : When semi-circular sheet is bent to form an open conical cup, the radius of the sheet becomes slant height of the cup and the semi-circular part of the sheet becomes the circumference of the base of the cone. ∴ Slant height of the ... 3 x 22/7 x 7 x 7 x 7√3 = 1078/3.√3 = 359.3 x 1.732 = 622.31 cm3

If a circular sheet of perimeter 2πr touching each side of a given quadrilateral sheet of perimeter 2p -Maths 9th

Description : If a circular sheet of perimeter 2πr touching each side of a given quadrilateral sheet of perimeter 2p -Maths 9th

Last Answer : Let ABCD be the quadrilateral from which a circular sheet is cut off touching each side of the quadrilateral. Also, given AB + BC + CD + DA = 2p ...(i) Circumference of the circle = 2πr ⇒ ... = pr.∴ Required remaining area = Area of quadrilateral - Area of circle = pr - πr2 = r(p - πr).

A goat is tethered to one end of a rope of length 20m, while the other end is fixed at the centre of a large circular field. -Maths 9th

Description : A goat is tethered to one end of a rope of length 20m, while the other end is fixed at the centre of a large circular field. -Maths 9th

Last Answer : (b) 3.5 x 100πThe goat can graze the area CABEODC + quarter circle CDF + quarter circle FEB= \(rac{3}{4}\)x π x (20)2 + \(rac{1}{4}\) x π x (10)2 + \(rac{1}{4}\) x π x (10)2 = 300π + 25π + 25π= 3.5 x 100π.

There are 10 persons who are to be seated around a circular table. Find the probability that two particular persons will always sit together. -Maths 9th

Description : There are 10 persons who are to be seated around a circular table. Find the probability that two particular persons will always sit together. -Maths 9th

Last Answer : Total number of ways in which 10 person can sit around a circular table = 9! (∵ We shall keep one place fixed and the rest of the 9 places will be filled in (9 8 7 6 5 4 3 2 1) ways asthere is ... probability = \(rac{2 imes8!}{9!}\) = \(rac{2 imes8!}{9 imes8!}\) = \(rac{2}{9}.\)

In how many ways can 8 people sit around a circular Table? (a) 5040 (b) 40320 (c) 20160 (d) 2520 -Maths 9th

Description : In how many ways can 8 people sit around a circular Table? (a) 5040 (b) 40320 (c) 20160 (d) 2520 -Maths 9th

Last Answer : As is known in case of circular permutations, we keep one place fixed, so 8 people can sit around a circular table in (8 – 1) ! ways = 7! ways = 5040 ways.

There are 6 numbered chairs placed around a circular table. 3 boys and 3 girls want to sit on them such that neither of two boys nor two girls -Maths 9th

Description : There are 6 numbered chairs placed around a circular table. 3 boys and 3 girls want to sit on them such that neither of two boys nor two girls -Maths 9th

Last Answer : Since the chairs are numbered, so they are distinguishable. Therefore 3 boys can be arranged on 3 alternate chairs in 3! ways. 3 girls can be arrenged in 3! ways Also, the girls can be seated before the boys. Total number of required ways = 3! × 3! + 3! × 3! = 2 × (3!)2

The outer and inner diameters of a circular pipe are 6 cm and 4 cm respectively. If its length is 10 cm, then what is the total surface -Maths 9th

Description : The outer and inner diameters of a circular pipe are 6 cm and 4 cm respectively. If its length is 10 cm, then what is the total surface -Maths 9th

Last Answer : answer:

50 circular plates each of radius .... Find its total surface area -Maths 9th

Description : 50 circular plates each of radius .... Find its total surface area -Maths 9th

Last Answer : 50 circular plate diameter of plate =14cm Radius of plate = d/2=214​=7cm thickness =0.5cm → Height of the cylinder = No. of plates × thickness of plate =50×0.5 =25cm → total surface Area = curved surface + 2 × area of base =2πr.h+2×πr2 =2πr(h+r) =2π×7(25+7) =2×722​×7×32 =1408cm2

the curved surface area of a cylinder is 154 cm. the total surface area of the cylinder is three times its curved surface area. find the volume of the cylinder. -Maths 9th

Description : the curved surface area of a cylinder is 154 cm. the total surface area of the cylinder is three times its curved surface area. find the volume of the cylinder. -Maths 9th

Last Answer : T.S.A = 3*154 = 462 cm² C.S.A = 154 cm² C.S.A = 2πrh T.S.A = 2πr(r+h) Now, In T.S.A = 2πrr + 2πrh 462 = 2πrr + 2πrh 462 = 2*22/7*r*r + 154 462 - 154 = 2*22/7*r*r 308*7/2*22 = r*r 49 = r*r R = 7 cm ... 7*h 154/44 = h 7/2 =h H = 3.5 cm or 7/2 cm Now volume = πrrh = 22/7 * 7* 7 *7/2 = 11*49 = 539 cm³

case study questions class 9 maths surface area and volume -Maths 9th

Description : case study questions class 9 maths surface area and volume -Maths 9th

Last Answer : Q. Read the source or text given below and answer the following questions: A conical circus tent has to be made with a cloth that is 5m wide, whose height is 24m, and the radius of the base is 7m. ... 4. Find the Curved Surface Area Answers: 1. Curved Surface Area 2. 550 m 3. Rs.3850 4.110m²

A matchbox measures 4 cm×2.5cm×1.5cm. What will be the volume of a packet containing 12 such boxes? -Maths 9th

Description : A matchbox measures 4 cm×2.5cm×1.5cm. What will be the volume of a packet containing 12 such boxes? -Maths 9th

Last Answer : Dimensions of a matchbox (a cuboid) are l×b×h = 4 cm×2.5 cm×1.5 cm respectively Formula to find the volume of matchbox = l×b×h = (4×2.5×1.5) = 15 Volume of matchbox = 15 cm3 Now, volume of 12 such matchboxes = (15×12) cm3 = 180 cm3 Therefore, the volume of 12 matchboxes is 180cm3.

Two cubes of side 2 cm each are joined end to end. Find the volume of the cuboid so formed. -Maths 9th

Description : Two cubes of side 2 cm each are joined end to end. Find the volume of the cuboid so formed. -Maths 9th

Last Answer : When two cubes of side 2 cm each are joined end to end then, Length (l) = (2 + 2) = 4cm Breadth (b) = 2 cm; Height (h) = 2 cm ∴ Volume of cuboid = lbh = 4 x 2 x 2 = 16 cm3

A metallic sheet is of rectangular shape with dimensions 48 cm x 36 cm. From each of its corners, a square of 8 cm is cut-off and an open box is made of the remaining sheet. Find the volume of the box. -Maths 9th

Description : A metallic sheet is of rectangular shape with dimensions 48 cm x 36 cm. From each of its corners, a square of 8 cm is cut-off and an open box is made of the remaining sheet. Find the volume of the box. -Maths 9th

Last Answer : When squares of 8 cm is cutt-off from rectangulare sheet then, Length of box (l) = (98 - 8 - 8) = 32 cm Breadth of box (b) = (36 - 8 - 8) = 20 cm Height of box (h) = 8cm ∴ Volume of box = lbh = 32 x 20 x 8 = 5120 cm3

The whole surface area of a rectangular block is 1300 cm2. Find its volume, if their dimensions are in the ratio of 4 : 3 : 2. -Maths 9th

Description : The whole surface area of a rectangular block is 1300 cm2. Find its volume, if their dimensions are in the ratio of 4 : 3 : 2. -Maths 9th

Last Answer : Let the length, breadth and height of the rectangular box be 4x, 3x and 2x, respectively. ∵ Total surface area = 1300 cm2 2(4x × 3x + 3x × 2x + 4x × 2x) = 1300 52x2 =1300x2 = 25x = 5 ∴ Volume of rectangular box = 4x × 3x × 2x = 24(5)2 = 3000 cm3

If the ratio of curved surface area and total surface area of a cylinder is 1 : 3, then find the volume of cylinder when the height is 2 cm. -Maths 9th

Description : If the ratio of curved surface area and total surface area of a cylinder is 1 : 3, then find the volume of cylinder when the height is 2 cm. -Maths 9th

Last Answer : Let the radius and height of the cylinder be r and h, respectively . Given that, Curved surface area / Total surface area = 1/3 ⇒ 2πrh / 2πr(h + r) = 1/3 ⇒ 3h = h + r ⇒ r = 2h = 4cm ∴ volume of cylinder πr2h = π × (4)2 × 2 = 32π cm3

If a sphere is inscribed in a cube, then find the ratio of the volume of the cube to the volume of the sphere. -Maths 9th

Description : If a sphere is inscribed in a cube, then find the ratio of the volume of the cube to the volume of the sphere. -Maths 9th

Last Answer : The ratio of the volume of the cube to the volume of the sphere are as

Calculate the edge of the cube if its volume is 1331 cm3 -Maths 9th

Description : Calculate the edge of the cube if its volume is 1331 cm3 -Maths 9th

Last Answer : Let the edge of the cube be a Volume of a cube = a×a×a 1331= a×a×a 11 =a ( as 1331 is the cube of 11 Therefore , Edge of a cube is 11 cm

Find the volume of cone of radius r/2 and height ‘2h’. -Maths 9th

Description : Find the volume of cone of radius r/2 and height ‘2h’. -Maths 9th

Last Answer : Volume of cone = 1 / 3π × (r / 2)2 × 2h = 1 / 3π × r2 / 4 × 2h = 1 / 6 πr2h cu. units.