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Question

a) What is the volume of a solid metal cylinder of height 4 centimetres and radius 5 centimetres?
b) This solid is melted and recast in to 5 cones of equal height and radius 2 centimetres. Find the height of such a cone.

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Solution

(a) Height of cylinder, h=4cm
Radius of cylinder, r=5 cm
Volume of cylinder =πr2h
=3.14×52×4 cm3
=314 cm3
(b) Radius of re-casted cone, r=2 cm
Let, height of re-casted cone =h
Volume of each cone =3145 cm3=62.8 cm3
Volume of cone =13πr2h

62.8=13×3.14×(2)2×h

h=62.8×34×3.14 cm
h=15 cm
Height of the cone is 15 cm.

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