Question

A vessel is in the form of a hemispherical bowl surmounted by a hollow
cylinder. The diameter of the hemisphere is 21 cm and the total height
of the vessel is 14.5 cm. Find its capacity.​

Answer 1

SOLUTION:-

Given:

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder.

•The diameter of the hemisphere is 21cm.

•The total height of the vessel is 14.5cm.

To find:

Find its Capacity.

Explanation:

•Dimeter=21

•Radius= 21/2cm

Capacity of a bowl:

Volume of hemisphere+volume of cylinder

formula of the volume of hemisphere;

$= \frac{2}{3} \pi {r}^{3}$

&

Volume of cylinder:

=) πr²h

According to the question:

$= > \frac{2}{3} \times \pi \times ( \frac{21}{2} ) \times (\frac{21}{2} ) \times ( \frac{21}{2} ) + \pi \times \frac{21}{2} \times \frac{21}{2} \times 14.5 \\ \\ = > 2 \times \frac{22}{7} \times \frac{7}{2} \times \frac{21}{2} \times \frac{21}{2} + \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times 14.5 \\ \\ = > \frac{44}{2} \times \frac{441}{4} + 11 \times 3 \times \frac{21}{2} \times 14.5 \\ \\ = > \frac{11 \times 441}{2} + \frac{10048.5}{2} \\ \\ = > \frac{4851}{2} + \frac{10048.5}{2} \\ \\ = > \frac{4851 + 10048.5}{2} \\ \\ = > \frac{14899.5}{2} {cm}^{3} \\ \\ = > 7449.75 { {cm} }^{3}$

Thus,

The capacity is 7449.75cm³.