Question

The amount of water displaced by a solid spherical ball of diameter $4.2$ cm, when it is completely immersed in water, is

• A. $38.808$ cm${}^3$
• B. $14.808$ cm${}^3$
• C. $58.808$ cm${}^3$
• D. $45.808$ cm${}^3$

Answer 1

The correct option is A $38.808$ cm${}^3$

The amount of water displaced by a solid spherical ball when it is completely immersed in water is equal to its volume.
Volume of a sphere of radius $r$ is $\frac{4}{3}\pi r^3$
As the diameter of the ball is $4.2$ cm, its radius $r=2.1$ cm
Hence, volume of water displaced $=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times 2.1\times 2.1\times 2.1=38.808$ cm${}^3$