Question

Calculate the volume of the hemisphere.

a) \[1095.23\;c{m^3}\]
b) \[2095.23\;c{m^3}\]
c) \[3095.23\;c{m^3}\]
d) \[4095.23\;c{m^3}\]

Answer 1

Hint: We are given a hemisphere in the figure and we have to find the volume of this hemisphere. We know, Volume of the Hemisphere \[ = \dfrac{2}{3}\pi {r^3}\], where \[r\] is the radius of the hemisphere. Here, we are given the radius of the sphere to be equal to \[10\;cm\]. We will use the above formula to find the Volume of the Hemisphere. And, then we will substitute the value of \[\pi \]which is equal to \[\dfrac{{22}}{7} = 3.14\] (Approximately).

Complete step-by-step answer:
We are given the radius of the Hemisphere to be equal to \[10\;cm\].
Using the formula for Volume of the Hemisphere, we have
Volume of the Hemisphere \[ = \dfrac{2}{3}\pi {r^3}\]
where \[r\]is the radius of the Hemisphere.
Radius of Hemisphere\[ = r = 10\;cm\]
\[\therefore \]Volume of the Hemisphere\[ = \dfrac{2}{3}\pi {(10)^3}\]$cm^3$
\[ = \dfrac{2}{3}\pi (1000)\] $cm^3$
 [Because \[({10^3} = 1000)\] and after opening brackets.]
\[ = \dfrac{2}{3} \times \pi \times 1000\]
\[ = \dfrac{{2000\pi }}{3}\]
Now, substituting the value of \[\pi = \dfrac{{22}}{7}\]in the above equation, we get
Volume of the Hemisphere \[ = \dfrac{{2000 \times \dfrac{{22}}{7}}}{3}\] $cm^3$
\[ = \left( {2000 \times \dfrac{{22}}{7}} \right) \div 3\]
[As \[a \div b = \dfrac{a}{b} = a \times \dfrac{1}{b}\]]
\[ = \left( {2000 \times \dfrac{{22}}{7}} \right) \times \dfrac{1}{3}\]
\[ = 2000 \times \dfrac{{22}}{7} \times \dfrac{1}{3}\]
\[ = \dfrac{{2000}}{1} \times \dfrac{{22}}{7} \times \dfrac{1}{3}\]
\[ = \dfrac{{2000 \times 22}}{{7 \times 3}}\]
 (Multiplying Numerators and Denominators respectively)
\[ = \dfrac{{44000}}{{21}}\]
\[ = 2095.23\] $cm^3$
Hence, we got Volume of the Hemisphere \[ = 2095.23\] $cm^3$
So, the correct answer is “Option b”.

Note: First of all, we need to remember the formula for Volume of the Hemisphere. Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance or 3D shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre.