Question

If the circumference of base of a hemisphere is \[2\pi \] then its volume ……………….\[c{m^3}\]
A. \[\dfrac{{2\pi }}{3}{r^3}\]
B. \[\dfrac{{2\pi }}{3}\]
C. \[\dfrac{{8\pi }}{3}\]
D. \[\dfrac{\pi }{{12}}\]

Answer 1

Hint: The volume of the hemisphere is given by \[\dfrac{{2\pi }}{3}{r^3}\] , where ‘\[r\]’ is the radius of the hemisphere. Circumference of the hemisphere is given by \[2\pi r\], where ‘\[r\]’ is the radius of the hemisphere. So, use this concept to reach the solution of the problem.

Complete step-by-step answer:

Given the circumference of base of a hemisphere is \[2\pi \]
But circumference of the hemisphere is given by \[2\pi r\]
By comparing the above data, we have
\[
   \Rightarrow 2\pi r = 2\pi \\
  \therefore r = 1cm \\
\]
So, the radius of the hemisphere is 1 cm.
Now, volume of the sphere is given by \[V = \dfrac{{2\pi }}{3}{r^3}\]
\[
   \Rightarrow V = \dfrac{{2\pi }}{3}{\left( 1 \right)^3} \\
   \Rightarrow V = \dfrac{{2\pi }}{3} \times 1 \\
  \therefore V = \dfrac{{2\pi }}{3}c{m^3} \\
\]
Thus, the correct option is B. \[\dfrac{{2\pi }}{3}\]

Note: In math, a hemisphere is defined as a three-dimensional shape that’s half of a sphere with one flat, circular side. Always mention the units after writing the answer. Here the units of volume is \[c{m^3}\].