Question

Find the amount of water displaced by a solid spherical ball of diameter 4.2m, when it is completely immersed in water.

• A. $58.31c{m}^3$
• B. $29.74c{m}^3$
• C. $38.81c{m}^3$
• D. $74.51c{m}^3$

Answer 1

The correct option is C $38.81c{m}^3$

Given, diameter of the solid spherical ball = 4.2 cm
$\therefore$ Radius of the solid spherical ball, $r=\frac{4.2}{2}=2.1cm$
Now, volume of water displaced by a solid spherical ball when it is completely immersed in water = Volume of the solid spherical ball
$=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (2.1{)}^3$
$=\frac{4}{3}\times \frac{22}{7}\times 2.1\times 2.1\times 2.1$
$=\frac{814.968}{21}=38.808=38.81c{m}^3$
Hence, the volume of water displaced by a solid spherical ball when it is completely immersed in water is $38.81c{m}^3$.