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

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 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

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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.

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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

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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 cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. -Maths 9th

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A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. -Maths 9th

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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.

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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

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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 sphere and a cone have equal bases. If their heights are also equal, the ratio of their curved surface will be : -Maths 9th

Description : A sphere and a cone have equal bases. If their heights are also equal, the ratio of their curved surface will be : -Maths 9th

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Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find (i) radius of the base -Maths 9th

Description : Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find (i) radius of the base -Maths 9th

Last Answer : Slant height of cone, l = 14 cm Let the radius of the cone be r. (i) We know, CSA of cone = πrl Given: Curved surface area of a cone is 308 cm2 (308 ) = (22/7) r 14 308 = 44 r r = 308 ... Total surface area of cone = 308+(22/7) 72 = 308+154 Therefore, the total surface area of the cone is 462 cm2.

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Description : How much ice-cream can be put into a cone with base radius 3.5 cm and height 12 cm ? -Maths 9th

Last Answer : Here, radius (r) = 3.5 cm and height (h) = 12 cm ∴ Amount of ice cream = 1 / 3 πr2h = 1 / 3 × 22 / 7 × 3.5 × 3.5 × 12 = 154 cm3

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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.

How much ice-cream can be put into a cone with base radius 3.5 cm and height 12 cm ? -Maths 9th

Description : How much ice-cream can be put into a cone with base radius 3.5 cm and height 12 cm ? -Maths 9th

Last Answer : Here, radius (r) = 3.5 cm and height (h) = 12 cm ∴ Amount of ice cream = 1 / 3 πr2h = 1 / 3 × 22 / 7 × 3.5 × 3.5 × 12 = 154 cm3

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.

The total surface area of a cone whose radius is r/2 and slant height 2l is -Maths 9th

Description : The total surface area of a cone whose radius is r/2 and slant height 2l is -Maths 9th

Last Answer : Total surface area of cone = πr(r+l) Given, radius = r/2​ and slant height = 2l Therefore, new total surface area of cone = πr/2​(r​/2+2l) = π(r/4^2​+rl) = πr(l+r/4​)

The total surface area of a cone whose radius is r/2 and slant height 2l is -Maths 9th

Description : The total surface area of a cone whose radius is r/2 and slant height 2l is -Maths 9th

Last Answer : Radius (r)=r/2 & slant height=2l TSA (S)=PIE R (l+r) =22/7×r/2(2l+r/2) =11/7×r(2l+r/2)

The radius and slant height of a cone... -Maths 9th

Description : The radius and slant height of a cone... -Maths 9th

Last Answer : Let the radius of cone (r) = 4x cm and the slant height of the cone (l) = 7x cm Curved surface area of cone = πrl ∴ πrl = 792 cm2 ⇒ 22/7 x 4x x 7x = 792 ⇒ x2 = 792/22 x 4 = 9 ⇒ x = 3 cm ∴ Radius of the cone = 4 x 3 = 12 cm

The radius and height of a cone are in the ratio 3 : 4 -Maths 9th

Description : The radius and height of a cone are in the ratio 3 : 4 -Maths 9th

Last Answer : Let the radius ofthe cone (r) = 3x cm Height of the cone (h) = 4x cm Volume of the cone = 1/3 πr2h ⇒ 301.44 = 1/3 x 3.14 x (3x)2 .4x ⇒ x3 = 301.44/3.14 x 12 = 8 ⇒ x3 = 23 ⇒ x = 2 ... 4 x 2 = 8 cm Slant height of the cone (l) = root under (√r2 + h2 ) = root under (√62 + 82)= √100 = 10 cm

A cone of height 7 cm and base radius 1 cm is carved from a cuboidal block of wood 10 cm × 5 cm × 2 cm -Maths 9th

Description : A cone of height 7 cm and base radius 1 cm is carved from a cuboidal block of wood 10 cm × 5 cm × 2 cm -Maths 9th

Last Answer : 92239223% Volume of cone = 1313πr2h = 13×227×1×7=22313×227×1×7=223 cu. cm Volume of cubical block = (10 × 5 × 2) cm3 = 100 cm3 ∴ Wastage of wood = (100−227)100×100(100−227)100×100 = 27832783% = 92239223%

Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m -Maths 9th

Description : Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m -Maths 9th

Last Answer : Radius of cone, r = 24/2 m = 12m Slant height, l = 21 m Formula: Total Surface area of the cone = πr(l+r) Total Surface area of the cone = (22/7)×12×(21+12) m2 = 1244.57m2

Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area -Maths 9th

Description : Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area -Maths 9th

Last Answer : Radius of the base of cone = diameter/ 2 = (10.5/2)cm = 5.25cm Slant height of cone, say l = 10 cm CSA of cone is = πrl = (22/7)×5.25×10 = 165

A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. -Maths 9th

Description : A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. -Maths 9th

Last Answer : Given: Radius of cone, r = diameter/2 = 40/2 cm = 20cm = 0.2 m Height of cone, h = 1m Slant height of cone is l, and l2 = (r2+h2) Using given values, l2 = (0.22+12) = (1.04) Or l ... (32.028 12) = Rs.384.336 = Rs.384.34 (approximately) Therefore, the cost of painting all these cones is Rs. 384.34.

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. -Maths 9th

Description : A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. -Maths 9th

Last Answer : Diameter of cone = 10.5 m Radius of cone (r) = 5.25 m Height of cone (h) = 3 m Volume of cone = 1 / 3 πr2h = 1 / 3 × 22 / 7 × 5.25 × 5.25 × 3 = 86.625m3 Cost of 1m3 of wheat = 10 ∴ Cost of 86.625 m3 of wheat = 10 × 86.625 = 86.625

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. -Maths 9th

Description : A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. -Maths 9th

Last Answer : Diameter of cone = 10.5 m Radius of cone (r) = 5.25 m Height of cone (h) = 3 m Volume of cone = 1 / 3 πr2h = 1 / 3 × 22 / 7 × 5.25 × 5.25 × 3 = 86.625m3 Cost of 1m3 of wheat = 10 ∴ Cost of 86.625 m3 of wheat = 10 × 86.625 = 86.625

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.

The radius of a right circular cone is 3 cm and its height is 4 cm. The curved surface of the cone will be (1) 12 sq. cm (2) 15 sq. cm (3) 18 sq. cm (4) 21 sq. cm

Description : The radius of a right circular cone is 3 cm and its height is 4 cm. The curved surface of the cone will be (1) 12 sq. cm (2) 15 sq. cm (3) 18 sq. cm (4) 21 sq. cm

Last Answer : (2) 15 sq. cm

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 square has its side equal to the radius of the sphere. The square revolves round a side to generate a surface of total area S. -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

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.

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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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 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%.

A sphere is cut into two equal halves and both the halves are painted from all the sides. The radius of the sphere is r unit and the -Maths 9th

Description : A sphere is cut into two equal halves and both the halves are painted from all the sides. The radius of the sphere is r unit and the -Maths 9th

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The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes. -Maths 9th

Description : The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes. -Maths 9th

Last Answer : Let r1 and r2 be radii of two cyclinder and V1, V2 be their volume . Let h be height of the two cyclinders, then V1 = πr2h and V2 = πr22h ∴ V1 / V2 = πr12h / πr22h = r12 / r22 = 16 / 25 .

The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes. -Maths 9th

Description : The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes. -Maths 9th

Last Answer : Let r1 and r2 be radii of two cyclinder and V1, V2 be their volume . Let h be height of the two cyclinders, then V1 = πr2h and V2 = πr22h ∴ V1 / V2 = πr12h / πr22h = r12 / r22 = 16 / 25 .

If the volume of a sphere is numerically equal to its surface area, then find the diameter of the sphere. -Maths 9th

Description : If the volume of a sphere is numerically equal to its surface area, then find the diameter of the sphere. -Maths 9th

Last Answer : Let r be the radius of the sphere. and Volume of a sphere = surface area of the sphere ⇒ 4 / 3πr3 = 4πr2 ⇒ r = 3 cm ∴ Diameter of the sphere = 2r = 2 × 3 = 6 cm

If the volume of a sphere is numerically equal to its surface area, then find the diameter of the sphere. -Maths 9th

Description : If the volume of a sphere is numerically equal to its surface area, then find the diameter of the sphere. -Maths 9th

Last Answer : Let r be the radius of the sphere. and Volume of a sphere = surface area of the sphere ⇒ 4 / 3πr3 = 4πr2 ⇒ r = 3 cm ∴ Diameter of the sphere = 2r = 2 × 3 = 6 cm

Which one of the following statements is correct? (A) (B) The cone subtended by an area on the sphere at the centre, is called the solid angle (C) The solid angle is equal to the ratio of the area on the sphere and the square of the radius of the sphere (D) All of these

Description : Which one of the following statements is correct? (A) (B) The cone subtended by an area on the sphere at the centre, is called the solid angle (C) The solid angle is equal to the ratio of the area on the sphere and the square of the radius of the sphere (D) All of these

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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

A cube and a sphere are of the same height. -Maths 9th

Description : A cube and a sphere are of the same height. -Maths 9th

Last Answer : Volume of cube/ volume of the sphere = a3 / 4/3.π.(a/2)3 = 6/π (Let edge of cube be a then radius of sphere = a/2) ∴ Required ratio = 6 : π

Select the incorrect statement from the following [ A ] Reinforcing bars in a column should not be less than 12 mm in diameter [ B ] The number of longitudinal bars in a circular column should not exceed four [ C ] The minimum percentage of longitudinal steel in columns should be 0.8% [ D ] None of the above

Description : Select the incorrect statement from the following [ A ] Reinforcing bars in a column should not be less than 12 mm in diameter [ B ] The number of longitudinal bars in a circular column should not ... The minimum percentage of longitudinal steel in columns should be 0.8% [ D ] None of the above

Last Answer : [ B ] The number of longitudinal bars in a circular column should not exceed four

A cone is 8.4 cm high and the radius of its base is 2.1 cm. -Maths 9th

Description : A cone is 8.4 cm high and the radius of its base is 2.1 cm. -Maths 9th

Last Answer : Volume of cone = Volume of sphere 1 / 3π(2.1)2 × 8.4 = 4 / 3 πr3 ⇒ r3 = (2.1)2 × 8.4 / 4 = (2.1)3 ⇒ r = 2.1 cm ∴ Radius of the sphere = 2.1 cm

A cone is 8.4 cm high and the radius of its base is 2.1 cm. -Maths 9th

Description : A cone is 8.4 cm high and the radius of its base is 2.1 cm. -Maths 9th

Last Answer : Volume of cone = Volume of sphere 1 / 3π(2.1)2 × 8.4 = 4 / 3 πr3 ⇒ r3 = (2.1)2 × 8.4 / 4 = (2.1)3 ⇒ r = 2.1 cm ∴ Radius of the sphere = 2.1 cm