Question

If a cylindrical vessel has a hemispherical bottom with radius 4 cm and height 15 cm, then its volume is .

• A. $686.4c{m}^3$
• B. $885.6c{m}^3$
• C. $445c{m}^3$
• D. $795c{m}^3$

Answer 1

The correct option is A $686.4c{m}^3$

Given,
Radius of the hemisphere = 4 cm
Height of the vessel = 15 cm
$\Rightarrow$ Height of the cylindrical part = 15 cm - 4 cm = 11 cm

Now, volume of the vessel = Volume of hemisphere + Volume of cylinder

Volume of the hemisphere $=\frac{2}{3}\pi r^3$
$=\frac{2}{3}\pi \times 4^3$
$=\frac{2\pi }{3}\times 64$
$=42.6\pi c{m}^3$

Volume of the cylinder $=\pi r^{2}h$
$=\pi \times 4^2\times 11$
$=176\pi c{m}^3$

Volume of the vessel
$=176\pi c{m}^3+42.6\pi c{m}^3$
$=218.6\pi c{m}^3$
$=686.4c{m}^3$
$\therefore$ Volume of the vessel = $686.4c{m}^3$