Question

Find the volume of the sphere whose radius is
A) 7 cm
B) 0.63 m

Answer 1

Hint: Here, we need to find the volume of the spheres with the given radius. We will calculate the volume of the spheres by substituting the value of the radius in the formula for the volume of a sphere $\dfrac{4}{3}\pi {r^3}$ where r is the radius of the sphere.

Complete step-by-step answer:
(i) We will calculate the volume of the sphere by substituting the value of the radius in the formula for the volume of a sphere.
The radius of the sphere is 7 cm.
So, we get
$r = 7cm$
Now we will use the formula to get the volume of a sphere.
$ \Rightarrow $Volume of the sphere $ = \dfrac{4}{3}\pi {r^3}$
Substitute $r = 7$ in the formula,
$ \Rightarrow $Volume of the sphere $ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times {\left( 7 \right)^3}{\text{c}}{{\text{m}}^{\text{3}}}$
Rewriting the expression, we get,
$ \Rightarrow $Volume of the sphere $ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times 7 \times 7 \times 7{\text{c}}{{\text{m}}^{\text{3}}}$
Cancel out the common factors,
$ \Rightarrow $Volume of the sphere $ = \dfrac{4}{3} \times 22 \times 7 \times 7{\text{c}}{{\text{m}}^{\text{3}}}$
Multiplying the terms in the expression, we get
$\therefore $Volume of the sphere $ = \dfrac{{4312}}{3}{\text{c}}{{\text{m}}^{\text{3}}}$
We can write this in decimal format as
$\therefore $Volume of the sphere $ = 1437.33{\text{c}}{{\text{m}}^{\text{3}}}$
Hence, the volume of the sphere is $\dfrac{{4312}}{3}{\text{c}}{{\text{m}}^3}$ or $1437.33{\text{c}}{{\text{m}}^3}$.
(ii) We will calculate the volume of the sphere by substituting the value of the radius in the formula for the volume of a sphere.
The radius of the sphere is 0.63 m.
So, we get
$r = 0.63m$
Now we will use the formula to get the volume of a sphere.
$ \Rightarrow $Volume of the sphere $ = \dfrac{4}{3}\pi {r^3}$
Substitute $r = 7$ in the formula,
$ \Rightarrow $Volume of the sphere $ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times {\left( {0.63} \right)^3}{{\text{m}}^{\text{3}}}$
Rewriting the expression, we get,
$ \Rightarrow $Volume of the sphere $ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times 0.63 \times 0.63 \times 0.63{{\text{m}}^{\text{3}}}$
Convert the decimal part into a fraction,
$ \Rightarrow $Volume of the sphere $ = \dfrac{4}{3} \times 22 \times \dfrac{{63}}{{100}} \times \dfrac{{63}}{{100}} \times \dfrac{{63}}{{100}}{{\text{m}}^{\text{3}}}$
Cancel out the common factors,
$ \Rightarrow $Volume of the sphere $ = 11 \times \dfrac{21}{{25}} \times \dfrac{{63}}{{100}} \times \dfrac{{63}}{{50}}{{\text{m}}^{\text{3}}}$
Multiplying the terms in the expression, we get
$\therefore $Volume of the sphere $ = \dfrac{{916839}}{{125000}}{{\text{m}}^{\text{3}}}$
We can write this in decimal format as
$\therefore $Volume of the sphere $ = 7.334712{{\text{m}}^{\text{3}}}$
Hence, the volume of the sphere is $\dfrac{{916839}}{{125000}}{{\text{m}}^{\text{3}}}$ or $7.334712{{\text{m}}^{\text{3}}}$.

Note: A sphere is a three-dimensional round solid figure in which every point on its surface is equidistant from its center. The fixed distance is called the radius of the sphere and the fixed point is called the center of the sphere. The space occupied by a sphere is called the volume of the sphere.
We need to use the units as given in the question. A common mistake in the second part of the question is to write the volume in ${{\text{m}}^{\text{3}}}$ instead of ${\text{c}}{{\text{m}}^{\text{3}}}$. This is not correct. Try to remember the formula of the sphere for solving these types of questions.