Question

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of a cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy if a right circular cylinder circumscribes ,the toy find the difference of the volumes of a cylinder of the toy.

Answer 1

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Answer 2

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Let BPC be the hemisphere and ABC be the cone standing on the base of the hemisphere as shown in the above figure.

The radius BO of the hemisphere (as well as of the cone) =( ½) × 4 cm = 2 cm.

So, volume of the toy = (⅔) πr3 + (⅓) πr2h

$\tt = (⅔) × 3.14 × 23 + (⅓)× 3.14 × 22 × 2$

$\tt = 25.12 cm^3$

Now, let the right circular cylinder EFGH circumscribe the given solid.

The radius of the base of the right circular cylinder = HP = BO = 2 cm, and its height is

$\tt EH = AO + OP = (2 + 2) cm = 4 cm$

So, the volume required = volume of the right circular cylinder – the volume of the toy

$\tt = (3.14 × 22 × 4 – 25.12) cm^3$

$\tt = 25.12 cm^3$

Hence, the required difference between the two volumes = 25.12 cm^3

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