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 height and r be the radius of the cylindrical vessel. Since the hemispherical portion is raised upward at the bottom, it reduces the capacity of the vessel.

Volume = Volume of cylinder − Volume of hemisphere

= `πr^2h - 2/3πr^3`

= `(πr^2)/3 (3h - 2r)`

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