Question

Find the volume and surface area of the sphere of radius \[2.1cm\] \[\left( {\pi = \dfrac{{22}}{7}} \right)\] .

Answer 1

Hint: We have to find the volume and the surface area of the sphere for the value of radius \[2.1cm\] . We solve this question using the concept of the formula of the volume and the surface area of the sphere . By directly substituting the value of the radius in the formula we will obtain the value of the volume and the surface area of the sphere .

Complete step-by-step answer:
Given :
The value of radius of the sphere is given as :
\[r = 2.1cm\]

Now , also know that the formulas for the volume of a sphere is given as :
\[V = \dfrac{4}{3}\pi {R^3}\]
Where \[V\] is the volume of the sphere , \[R\] is the radius of the sphere .
Substituting the values of radius of the sphere in the above formula , we get the value of volume as :
\[V = \dfrac{4}{3} \times \dfrac{{22}}{7} \times {\left( {2.1} \right)^3}\]
\[V = \dfrac{4}{3} \times \dfrac{{22}}{7} \times \dfrac{{21}}{{10}} \times \dfrac{{21}}{{10}} \times \dfrac{{21}}{{10}}\]
On further solving the expression , we get
\[V = \dfrac{{21}}{{10}} \times \dfrac{{21}}{{10}} \times \dfrac{{88}}{{10}}\]
\[V = \dfrac{{38808}}{{1000}}\]
Hence , we get the value of volume as :
\[V = 38.808{cm^3}\]
Now , also know that the formulas for the surface area of a sphere is given as :
\[A = 4\pi {R^2}\]
Where \[A\] is the surface area of the sphere , \[R\] is the radius of the sphere .
Substituting the values of radius of the sphere in the above formula , we get the value of surface area as :
\[A = 4 \times \dfrac{{22}}{7} \times {\left( {2.1} \right)^2}\]
\[A = 4 \times \dfrac{{22}}{7} \times \dfrac{{21}}{{10}} \times \dfrac{{21}}{{10}}\]
On further solving the expression , we get
\[A = 22 \times \dfrac{{21}}{{10}} \times \dfrac{{12}}{{10}}\]
\[A = \dfrac{{5544}}{{100}}\]
Hence , we get the value of surface area as :
\[A = 55.44{cm^2}\]
Hence , the value of the volume and the surface area of the sphere are \[38.808{cm^3}\] and \[55.44{cm^2}\] respectively .

Note: A sphere is a set of points in a three dimensional surface , it is such that all the points on the surface of the sphere are equidistant from the centre of the sphere . We need to be specific while using the formulas for sphere and hemisphere as that have little difference between them . If we cut the sphere into two parts we get two hemispheres .