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

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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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 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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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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There are two identical cubes. Out of one cube, a sphere of maximum volume (VS) is cut off. Out of the second cube, a cone of maximum volume -Maths 9th

Description : There are two identical cubes. Out of one cube, a sphere of maximum volume (VS) is cut off. Out of the second cube, a cone of maximum volume -Maths 9th

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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

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 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

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

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.

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.

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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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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A cone, a hemisphere and a cylinder -Maths 9th

Description : A cone, a hemisphere and a cylinder -Maths 9th

Last Answer : V1 (volume of cone) = 1/3 πr2r V2 (volume of hemisphere) = 2/3 πr3 V3 (volume of cylinder) = πr2 .r V1: V2: V3 = 1/3 πr3 : 2/3πr3 : πr3 = 1/3 : 2/3 : 1 V 1: V 2: V 3 = 1 : 2 : 3

A cylinder and a cone have equal -Maths 9th

Description : A cylinder and a cone have equal -Maths 9th

Last Answer : Curved surface area of cylinder/Curved surface area of cone = 2πrh/πrl = 2πrh/πr root under√(r2 + h2) 8/5 = 2h/root under√(r2 + h2) ⇒ 64/25 = 4h2/r2 + h2 ⇒ 64r2 + 64h2 = 100 h2 ⇒ 64r2 = 100h2 - 64h2 ⇒ 64r2 = 36h2 ⇒ r2/h2 = 36/64 = 9/16 ⇒ r/h = 3/4 ∴ r : h = 3 : 4

A cylinder, a cone and a sphere are of the same radius -Maths 9th

Description : A cylinder, a cone and a sphere are of the same radius -Maths 9th

Last Answer : Let r be the common radius of a cylinder, cone and a sphere. Then, height of the cylinder = Height of the cone = Height of the sphere = 2r Let 'I' be the slant height of the cone. Then l = root under( √r2 + h2) = root under( ... , S1 : S2 :S3 = 4 πr2 : √5 πr2 : 4 πr2 ∴ S1 : S2 : S3 = 4 : √5 : 4

A cylinder is within the cube touching all the vertical faces. A cone is inside the cylinder. If their heights are same with -Maths 9th

Description : A cylinder is within the cube touching all the vertical faces. A cone is inside the cylinder. If their heights are same with -Maths 9th

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A sphere, a cylinder and a cone respectively are of the same radius and same height. Find the ratio of their curved surfaces. -Maths 9th

Description : A sphere, a cylinder and a cone respectively are of the same radius and same height. Find the ratio of their curved surfaces. -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.

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.

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.

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

Last Answer : answer:

A metallic sheet is of rectangular shape with dimensions 28m × 36m. From each of its corners, a square is cut off so as to make an open box. -Maths 9th

Description : A metallic sheet is of rectangular shape with dimensions 28m × 36m. From each of its corners, a square is cut off so as to make an open box. -Maths 9th

Last Answer : R.E.F image Volume of box =l×b×h From the diagram l=48−2(8) ∵ Two square formed side =32m b=36−2(8) =20m Also h=8m from question ∴ Volume =32×20×8 =5120m3

Find the radius of the largest right circular cone that can be cut out from a cube of edge 4.2 cm. -Maths 10th

Description : Find the radius of the largest right circular cone that can be cut out from a cube of edge 4.2 cm. -Maths 10th

Last Answer : Radius of the largest right circular cone 1/2 (Edge of the Square) =4.2/2 = 2.1 cm

The circumference of the base of 9 m high wooden solid cone is 44 m. Find the slant height of the cone. -Maths 9th

Description : The circumference of the base of 9 m high wooden solid cone is 44 m. Find the slant height of the cone. -Maths 9th

Last Answer : Circumference of the base of a cone = 2πr

The circumference of the base of 9 m high wooden solid cone is 44 m. Find the slant height of the cone. -Maths 9th

Description : The circumference of the base of 9 m high wooden solid cone is 44 m. Find the slant height of the cone. -Maths 9th

Last Answer : Circumference of the base of a cone = 2πr

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

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.

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.

What is the volume of cone ? -Maths 9th

Description : What is the volume of cone ? -Maths 9th

Last Answer : 1/3 x π x r^2 x h

The C.G. of a right circular solid cone of height h lies at the following distance from the base (A) h/2 (B) J/3 (C) h/6 (D) h/4

Description : The C.G. of a right circular solid cone of height h lies at the following distance from the base  (A) h/2  (B) J/3  (C) h/6  (D) h/4 

Last Answer : (D) h/4 

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

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

Last Answer : Volume of cone = 1/3 πr2h = 1/3 x 22/7 x (3.5)2 x 12 cm3 = 154 cm3.

A solid cylinder has total surface area of 462 cm square. -Maths 9th

Description : A solid cylinder has total surface area of 462 cm square. -Maths 9th

Last Answer : Let r cm be the radius of the base and h cm be the height of the cylinder, Then, total surface area of cylinder = 2 πr (r + h) Curved surface area of cylinder = 2 πrh We have, Curved surface area = 1/3(Total surface ... x 22 = 7/2 cm Volume of the cylinder = πr2h = 22/7 x 7 x 7 x 7/2 = 539 cm3

The radius and height of a right circular cone are 28cm & 72 cm respectively. Find its volume.

Description : The radius and height of a right circular cone are 28cm & 72 cm respectively. Find its volume.

Last Answer : Answer: A 

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

In the following geometric primitives. which is not a solid entity of CSG modelling: a.Box b.Cone c.Cylinder d.Circle

Description : In the following geometric primitives. which is not a solid entity of CSG modelling: a.Box b.Cone c.Cylinder d.Circle

Last Answer : d.Circle

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

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

A spherical ball is divided into two equal halves. If the curved surface area of each half is 56.57 cm?, find the volume of the spherical ball.11531/cylinder-radius-halved-and-height-doubled-then-find-volume-with-respect-original-volume -Maths 9th

Description : A spherical ball is divided into two equal halves. If the curved surface area of each half is 56.57 cm?, find the volume of the spherical ball.11531/cylinder-radius-halved-and-height-doubled-then-find-volume-with-respect-original-volume -Maths 9th

Last Answer : since curved surface of half of the spherical ball = 56.57 cm2 ∴ 2πr2 = 56.57 ⇒ r2 = 56.57 / 2 × 3.14 = 9 ⇒ r = 3 cm Now, volume of spherical ball = 4 / 3 πr3 = 4 / 3 × 3.14 × 3 × 3 × 3 = 113.04 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

A spherical ball is divided into two equal halves. If the curved surface area of each half is 56.57 cm?, find the volume of the spherical ball.11531/cylinder-radius-halved-and-height-doubled-then-find-volume-with-respect-original-volume -Maths 9th

Description : A spherical ball is divided into two equal halves. If the curved surface area of each half is 56.57 cm?, find the volume of the spherical ball.11531/cylinder-radius-halved-and-height-doubled-then-find-volume-with-respect-original-volume -Maths 9th

Last Answer : since curved surface of half of the spherical ball = 56.57 cm2 ∴ 2πr2 = 56.57 ⇒ r2 = 56.57 / 2 × 3.14 = 9 ⇒ r = 3 cm Now, volume of spherical ball = 4 / 3 πr3 = 4 / 3 × 3.14 × 3 × 3 × 3 = 113.04 cm3

Define :Volume and surface area of a hollow cylinder. -Maths 9th

Description : Define :Volume and surface area of a hollow cylinder. -Maths 9th

Last Answer : answer:

A cylinder is filled to 4/5 th of its volume. It is, then tilted so that the level of water coincides with one edge of its bottom and top edge -Maths 9th

Description : A cylinder is filled to 4/5 th of its volume. It is, then tilted so that the level of water coincides with one edge of its bottom and top edge -Maths 9th

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The radius and height of a right circular cylinder are 42 cm & 63 cm respectively. Find its volume. a) 237564 cm3 b) 349272 cm3 c) 379252 cm3 d) 453213cm3

Description : The radius and height of a right circular cylinder are 42 cm & 63 cm respectively. Find its volume. a) 237564 cm3 b) 349272 cm3 c) 379252 cm3 d) 453213 cm3

Last Answer :  Answer: B 

From a wooden cylindrical block, whose diameter is equal to its height, a sphere of maximum possible volume is carved out. -Maths 9th

Description : From a wooden cylindrical block, whose diameter is equal to its height, a sphere of maximum possible volume is carved out. -Maths 9th

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A solid cube of side 12 cm is cut into -Maths 9th

Description : A solid cube of side 12 cm is cut into -Maths 9th

Last Answer : Volume of given cube = a3 = 123 = 12 x 12 x 12 cm3 Let the edge of the new cube = x ∴ Volume of new cube = x3 Volume of 8 new cubes = 8x3 Now, 8x3 = 12 x 12 x 12 ⇒ x 3 = 12 x 12 x 12/8 = 6 3 ⇒ x ... area of new cubes = 6a2/6x2 = 6 x 122/6 x 62 = 6 x 12 x 12/6 x 6 x 6 = 4/1 = 4 : 1

An equilateral triangle with side a is revolved about one of its sides as axis. What is the volume of the solid of revolution thus obtained ? -Maths 9th

Description : An equilateral triangle with side a is revolved about one of its sides as axis. What is the volume of the solid of revolution thus obtained ? -Maths 9th

Last Answer : answer: