Question

A test tube has radius 2.1 cm and height 16.1 cm. Volume of the test tube is .

• A. $324c{m}^3$
• B. $213.4c{m}^3$
• C. $516c{m}^3$
• D. $981c{m}^3$

Answer 1

The correct option is B $213.4c{m}^3$

A test tube has a cylindrical shape with a hemispherical base.


Given: Radius of the hemisphere = 2.1 cm
Height of the test tube = 16.1 cm
$\Rightarrow$ Height of the cylinder
= 16.1 - 2.1 = 14 cm

Volume of the test tube
= Volume of hemisphere + Volume of cylinder

Volume of hemisphere = $\frac{2}{3}\pi r^3$
= $\frac{2}{3}\times \frac{22}{7}\times \frac{21}{10}\times \frac{21}{10}\times \frac{21}{10}$

=$\frac{2\times 22\times 21\times 21}{1000}$

= $19.404c{m}^3$

Volume of cylinder = $\pi r^{2}h$
= $\frac{22}{7}\times \frac{21}{10}\times \frac{21}{10}\times 14$

= $\frac{22\times 3\times 21\times 14}{100}$

= $194.04c{m}^3$

Now, volume of test tube
= $19.404c{m}^3$ + $194.04c{m}^3$
= $213.44c{m}^3$
$\therefore$ Volume of the test tube is $213.44c{m}^3$.