Question

Find the volume of the sphere of the radius 11.2cm.

Answer 1

Hint: In this question, we have been given the value of the radius of the sphere and we have to calculate the volume of the sphere using the formula for the volume of the sphere, which is $\dfrac{4}{3}\pi {R^3}$
Substituting the value of the radius in the formula and simplifying it will use the value for the volume of the sphere.

Complete step-by-step answer:
Given data: Radius of the sphere$ = 11.2cm$

We know that the volume of the sphere with the radius ‘R’ is given by
The volume of the radius$ = \dfrac{4}{3}\pi {R^3}$
Therefore the volume of the given sphere$ = \dfrac{4}{3}\pi {(11.2)^3}$
On cubing the term in the bracket, we get,
$ = \dfrac{4}{3}\pi (1404.928)$
On Substituting the value of $\pi = \dfrac{{22}}{7}$ , we get,
$ = \dfrac{4}{3}\left( {\dfrac{{22}}{7}} \right)(1404.928)$
On further multiplying the terms in the bracket, we get,
$ = \dfrac{4}{3}\left( {\dfrac{{30908.416}}{7}} \right)$
On further simplifying the brackets, we get,
$ = \dfrac{{213633.664}}{{21}}$
On dividing the numerator by the denominator, we get,
$ = 5887.317\bar 3c{m^3}$
Hence the volume of the sphere is $5887.317\bar 3c{m^3}$.

Note: Here as the radius is given in centimeters the volume will be cubic centimeter, and you should never forget to write units of the given quantity.
We can also find the volume of the sphere in a cubic meter.
 We know that $1cm = {10^{ - 2}}m$
So, the radius is $11.2cm = 11.2 \times {10^{ - 2}}m$
Therefore the volume of the given sphere$ = \dfrac{4}{3}\pi {(11.2 \times {10^{ - 2}})^3}$
On cubing the term in the bracket
$ = \dfrac{4}{3}\pi (1404.928 \times {10^{ - 6}})$
Substituting the value of $\pi = \dfrac{{22}}{7}$
$ = \dfrac{4}{3}\left( {\dfrac{{22}}{7}} \right)(1404.928 \times {10^{ - 6}})$
On further multiplying the terms in the bracket
$ = \dfrac{4}{3}\left( {\dfrac{{30908.416}}{7} \times {{10}^{ - 6}}} \right)$
On further simplifying the brackets
$ = \dfrac{{213633.664}}{{21}}$ $ \times {10^{ - 6}}$
On dividing the numerator by the denominator
$ = 5887.317\bar 3 \times {10^{ - 6}}{m^3}$
Hence volume of sphere is $5887.317\bar 3 \times {10^{ - 6}}{m^3}$