Question

A solid is in the shape of a cylinder surmounted on a hemisphere. If the diameter and the total height of the solid are 21 cm and 25.5 cm respectively, then find its volume.

• A. 8623 cm${}^3$
• B. 7823 cm${}^3$
• C. 7623 cm${}^3$
• D. 7283 cm${}^3$

Answer 1

The correct option is C 7623 cm${}^3$

Let r and h be radius and height of the cylinder respectively.
Given, diameter of the hemisphere = 21 cm
So, radius of hemisphere (r) = $\frac{21}{2}$ = 10.5 cm
Given, height of the solid shape = 25.5 cm
Also, radius of hemisphere + height of the cylinder = 25.5 cm
So, 10.5 + h = 25.5
h = 25.5 - 10.5
h = 15 cm

To find the volume of the solid shape we have to find the sum of volume of hemisphere and volume of cylinder.

Volume of solid shape
= Volume of hemisphere + Volume of cylinder
= $\frac{2}{3}\pi r^3+\pi r^{2}h$
= $\pi r^2[\frac{2}{3}r+h]$
= $\frac{22}{7}\times (10.5{)}^2\times [\frac{2}{3}\times 10.5+15]$
= 22 x 1.5 x 10.5 x [ 2 x 3.5 + 15]
= 346.5 x 22
= 7623 cm${}^3$

Therefore, volume of the solid shape = 7623 cm${}^3$