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Surface Areas and Volumes

Short Answer Type

451. A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

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452. If the surface are as of two spheres are in the ratio 4 : 9, then find the ratio of their volumes.

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453. If two cones have their volumes in the ratio 3 :1 and their heights are in the ratio 1 : 3, then find the ratio of their radius.

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454. The radius of a solid hemispherical toy is 3.5 cm. Find the total surface area.

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455. If the number of square centimetres on the surface of a sphere is equal to the number of cubic centimetres in its volume, what is the diameter of the sphere?

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456. Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

Let V₁ and V₂ be the volume of the cube and sphere respectively, then
V₁= (2r)³ and V₂ =

4 over 3 comma space πr cubed

therefore space space space space straight V subscript 1 over straight V subscript 2 equals fraction numerator left parenthesis 2 straight r right parenthesis cubed over denominator begin display style 4 over 3 end style πr cubed end fraction equals fraction numerator 8 straight r cubed over denominator begin display style 4 over 3 end style πr cubed end fraction equals 6 over straight pi Hence comma space straight V subscript 1 space colon space straight V subscript 2 equals 6 space colon space straight pi

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457. A cylinder and a cone are of the same base radius and of same height. Find the ratio of the volume of cylinder to that of the cone.

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458. A right circular cylinder and a right circular cone have the same base radius and same height. What is the ratio of the volume of the cylinder to that of cone?

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459. Find the maximum volume of a cube that can be carved out of a solid hemisphere of radius r.

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460. A glass cylidner with diameter 20 cm has water to a height of 9 cm. A metal cube at 8 cm edge is immersed in it completely. Calculate the height by which water will rise in the cylinder.

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