Volume of Composite Solids


 
 
Concept Explanation
 

Volume of Composite Solids

A composite solid is a solid that is composed, or made up of, two or more solids.

Example: A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.

Solution: Let r be the radius of the hemisphere and h be the height of the conical part of the toy. Then, r  = 4.2 cm, height of cone = (10.2 - 4.2) cm = 6 cm. Also, radius of the base of the cone = 4.2 cm

large therefore    Volume of the wooden toy = Volume of the conical part + Volume of the hemispherical part =  large (frac{1}{3}pi r^{2}h + frac{2pi }{3}r^{3}) cm^{3} = large frac{pi r^{2}}{3}(h + 2r)cm^{3}

= large frac{1}{3}times frac{22}{7}times 4.2times 4.2 times (6+2times 4.2)cm^{3}

= large frac{1}{3}times frac{22}{7}times 4.2times 4.2 times 14.4 cm^{2} =266.11 cm^{3}

Sample Questions
(More Questions for each concept available in Login)
Question : 1

A solid is in the form of a cylinder surrounded by a cone. The heights of cone and the cylinder are 6 cm and 12 cm respectively. If the radius of the cone is 7 cm, its volume will be

Right Option : A
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Explanation
Question : 2

A cone and a cylinder are having the same base. Find the ratio of their heights if their volumes are equal.

Right Option : B
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Explanation
Question : 3

How many planks each of which is 2 m long, 2.5 cm broad and 4 cm thick can be cut-off from a wooden block 6 m long, 15 cm broad and 40 cm thick?

Right Option : B
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Explanation
 
 
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