Question

Find the volume of a sphere whose radius is
(i) 7 cm (ii) \[0.63\] 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 volume of a sphere.

Formula used: We will use the formula of 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 volume of a sphere.
The radius of the sphere is 7 cm.
Therefore, we get
\[r = 7\]cm
Now we will use the formula to get the volume of a sphere.
Substituting \[r = 7\]cm in the formula \[\dfrac{4}{3}\pi {r^3}\], we get
\[ \Rightarrow \] Volume of the sphere \[ = \dfrac{4}{3}\pi {\left( 7 \right)^3}{\text{ c}}{{\text{m}}^3}\]
Substituting \[\pi = \dfrac{{22}}{7}\] in the expression, we get
\[ \Rightarrow \] Volume of the sphere \[ = \dfrac{4}{3}\left( {\dfrac{{22}}{7}} \right){\left( 7 \right)^3}{\text{ c}}{{\text{m}}^3}\]
Rewriting the expression, we get
\[ \Rightarrow \] Volume of the sphere \[ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times 7 \times 7 \times 7{\text{ c}}{{\text{m}}^3}\]
Simplifying the expression, we get
\[ \Rightarrow \] Volume of the sphere \[ = \dfrac{4}{3} \times 22 \times 7 \times 7{\text{ c}}{{\text{m}}^3}\]
Multiplying the terms in the expression, we get
\[ \Rightarrow \] Volume of the sphere \[ = \dfrac{{4312}}{3}{\text{ c}}{{\text{m}}^3}\]
We can write this in decimal format as
\[ \Rightarrow \] Volume of the sphere \[ = 1437.33{\text{ c}}{{\text{m}}^3}\]
\[\therefore\] The volume of the sphere with radius 7 cm is \[\dfrac{{4312}}{3}{\text{ c}}{{\text{m}}^3}\] or \[1437.33{\text{ c}}{{\text{m}}^3}\].

(ii)The radius of the sphere is \[0.63\]m.
Therefore, we get
\[r = 0.63\]m
Substituting \[r = 0.63\]m in the formula \[\dfrac{4}{3}\pi {r^3}\], we get
\[ \Rightarrow \] Volume of the sphere \[ = \dfrac{4}{3}\pi {\left( {0.63} \right)^3}{{\text{m}}^3}\]
Substituting \[\pi = \dfrac{{22}}{7}\] in the expression, we get
\[ \Rightarrow \] Volume of the sphere \[ = \dfrac{4}{3}\left( {\dfrac{{22}}{7}} \right){\left( {0.63} \right)^3}{{\text{m}}^3}\]
Rewriting the expression, we get
\[ \Rightarrow \] Volume of the sphere \[ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times 0.63 \times 0.63 \times 0.63{\text{ }}{{\text{m}}^3}\]
\[ \Rightarrow \] Volume of the sphere \[ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times \dfrac{{63}}{{100}} \times \dfrac{{63}}{{100}} \times \dfrac{{63}}{{100}}{\text{ }}{{\text{m}}^3}\]
Simplifying the expression, we get
\[ \Rightarrow \] Volume of the sphere \[ = 11 \times \dfrac{3}{{25}} \times \dfrac{{63}}{{50}} \times \dfrac{{63}}{{100}}{\text{ }}{{\text{m}}^3}\]
Multiplying the terms in the expression, we get
\[ \Rightarrow \] Volume of the sphere \[ = \dfrac{{130977}}{{125000}}{\text{ }}{{\text{m}}^3}\]
We can write this in decimal format as
\[ \Rightarrow \] Volume of the sphere \[ = 1.047816{\text{ }}{{\text{m}}^3}\]
\[\therefore\] The volume of the sphere with radius \[0.63\] m is \[\dfrac{{130977}}{{125000}}{\text{ }}{{\text{m}}^3}\] or \[1.047816{\text{ }}{{\text{m}}^3}\].

Note: 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 \[{\text{c}}{{\text{m}}^3}\] instead of \[{{\text{m}}^3}\]. This is not correct. Try to remember the formula of the sphere for solving these types of questions.