Question

Find the volume of a sphere whose radius is :
i.7cm
ii.0.63cm

Answer 1

Hint: Use the formula for volume of sphere and then substitute the value of r to obtain the required value of volume.
Volume of a sphere = $4/3\pi {r^3}$

Complete step-by-step answer:

For r = 7 cm
We know,
Volume of a sphere = $4/3\pi {r^3}$
Substituting the value of r, we get:
 \[4/3\pi {r^3} = 4/3\pi {(7)^3}\]
\[
   = (4/3)(22/7) \times 7 \times 7 \times 7 \\
   = 4312/21 \\
 \]
 Volume \[ = 1437.33\]cm³

ii) For r = 0.63 m

   We know,
   Volume of a sphere = $4/3\pi {r^3}$
   Substituting the value of r, we get:
   \[4/3\pi {r^3} = 4/3\pi {(0.63)^3}\]
\[
   = (4/3)(22/7) \times 0.63 \times 0.63 \times 0.63 \\
   = (4/3)(22/7)(63/100)(63/100)(63/100) \\
 \]
(To remove decimal and make calculation easier)
\[ = 22004136/21000000\]
 Volume \[ = 1.0478\]m³
Therefore Volume of the sphere when radius= 7cm is 1437.33 cm3 and when radius is 0.63 cm, it is 1.0478 m³.

Note: Be very careful with the units, for the radius given in cm, the volume will be in cm3 and for m, the volume will be in m3.
A sphere is a three dimensional (3 – D) figure and in simple terms the boundary occupied by a 3 – D object is referred to as volume.
In the sphere, the width, circumference and mean curvature are constant.