Question

Find the volume of a sphere whose radius is
(i) \[7\]$cm$ (ii) $0.63$$m$
Use $\pi = \dfrac{{22}}{7}$.

Answer 1

Hint: The volume of a sphere is the capacity it has and it depends on the radius of sphere. To calculate the volume of a sphere, we use following formula:
Volume of a sphere=$ = \dfrac{4}{3}\pi {r^3}$ cubic units, where $r$ is the radius of the sphere.

Complete step-by-step answer:
(i) Given, Radius of the sphere $\left( r \right) = 7$$cm$
Volume of the sphere$ = \dfrac{4}{3}\pi {r^3}$
$ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times {\left( 7 \right)^3}$
$ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times 7 \times 7 \times 7$
$ = \dfrac{4}{3} \times 22 \times 1 \times 7 \times 7$
$ = \dfrac{{88 \times 49}}{3}$
$ = \dfrac{{4312}}{3}$
\[ = 1437.33\]$c{m^3}$
(ii) Given, Radius of the sphere $\left( r \right) = 0.63$$m$
Volume of the sphere$ = \dfrac{4}{3}\pi {r^3}$
$ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times {\left( {0.63} \right)^3}$
$ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times 0.63 \times 0.63 \times 0.63$
$ = 4 \times 22 \times 0.09 \times 0.21 \times 0.63$
\[ = 1.0478\]${m^3}$
$ = 1.05$${m^3}$

Additional Information: A sphere is a three dimensional round solid figure in which every point on its surface is equidistant from its centre. The fixed distance is called the radius of the sphere and the fixed point is called the centre of the sphere. The space occupied by a sphere is called the volume of the sphere.

Note: The volume of the sphere is always measured in cubic units, such as- $c{m^3}$ or ${m^3}$. Generally, we have found the volume of a sphere to 3 decimal places. Then we round the number to 2 decimal places according to what the number is at 3rd decimal place as we do in part(ii). For ex-
If it is $ < = 3.144$, then $3.14$;
If it is $ > = 3.145$, then $3.15$.