Question

Find the volume of a sphere whose radius is 11.2 cm.

Answer 1

Hint: Sphere is a 3 dimensional figure in which all points on it are at equal distance from a fixed point called center and this equal distance is called the radius of the sphere. Use the formula of volume of sphere i.e. $\dfrac{4}{3}\pi {r^3}$, where $r$ is the radius. Put the value of radius from the question and $\pi = \dfrac{{22}}{7}$ to get the final answer.

Complete step-by-step answer:
According to the question, the radius of the sphere is given as 11.2 cm. We have to determine its volume.
We know that the sphere is a 3 dimensional shape with all the points in it are at a constant distance from a fixed point called center and this fixed distance is called radius of the sphere.

Now, the volume of the sphere is given by the formula:
$ \Rightarrow V = \dfrac{4}{3}\pi {r^3}$, where $r$ is the radius of the circle.
Putting $r = 11.2{\text{ cm}}$ from the question, in the above formula, we’ll get:
$ \Rightarrow V = \dfrac{4}{3}\pi {\left( {11.2} \right)^3}$
Putting $\pi = \dfrac{{22}}{7}$ and ${\left( {11.2} \right)^3} = 1404.928$, we’ll get:
$ \Rightarrow V = \dfrac{4}{3} \times \dfrac{{22}}{7} \times 1404.928$
Simplifying it further, we’ll get:
$
   \Rightarrow V = \dfrac{{123633.664}}{{21}} \\
   \Rightarrow V = 5887.32 \\
$

Thus, the volume of the sphere is $5887.32{\text{ c}}{{\text{m}}^3}$.

Note: The formula of the surface area of the sphere is $4\pi {r^2}$. From this formula, we can conclude that the surface area of sphere varies with the square of its radius while from volume’s formula, $\dfrac{4}{3}\pi {r^3}$, we can say that its volume varies with the cube of its radius.
$ \Rightarrow {\text{ Surface Area}} \propto {r^2}$ and ${\text{Volume}} \propto {r^3}$
So, if the radius of the sphere becomes twice, the surface area will become 4 times of its initial value and volume will become 8 times of its initial value.