Question

Write True or False and justify your answer in the following.

The capacity of cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in fig. is πr³(3h – 2r) where r is radius in c³m and h cm is height.

Answer 1

This statement is false.

Explanation:

Let h be the total internal height and the hemisphere (radius r) projects upward into the cylinder, so the straight cylindrical part has height h – r.

Volume = Volume of cylinder πr²(h – r) + Volume of hemisphere `1/2 xx 4/3 πr^3 = 2/3 πr^3`.

Thus, `V = πr^2(h - r) + 2/3 πr^3` 

= `πr^2h - 1/3 πr^3`

= `πr^2h - r/3 cm^3`

The given expression πr³(3h – 2r) is incorrect and dimensionally inconsistent: it yields cm⁴, so the statement is false.