Question

Find the volume of a sphere-shaped metallic shotput having a diameter of 8.4cm. (Take, \[\pi =\dfrac{22}{7}\]).

Answer 1

Hint: Find the radius of the sphere by taking half of the diameter. Then substitute these values in the formula for finding the volume of the sphere.

Complete step-by-step answer:
We have to find the volume of a sphere- shaped metallic shot put. We have been given the diameter of the sphere. The diameter of the sphere is twice the radius of the sphere. So to get the radius of the sphere, take half of the diameter of the sphere.
Diameter of sphere = 2 \[\times \]radius of sphere.
We can take the diameter of the sphere as ‘d ’ and radius of sphere as ‘r’.
\[\begin{align}
  & \therefore d=2r \\
 & \therefore r=\dfrac{d}{2} \\
\end{align}\]
We have been given the radius of the sphere as 8.4cm.
Therefore, radius of sphere = diameter / 2 = 4.2cm.
Thus we got the radius of the sphere as 4.2cm.
Now, let us find the volume of the sphere.
We know the formula to find volume of sphere\[=\dfrac{4}{3}\pi {{r}^{3}}\].
We know, \[\pi =\dfrac{22}{7}\]and r = 4.2cm.
Let us substitute and find the volume of the sphere.
Volume of sphere \[=\dfrac{4}{3}\pi {{r}^{3}}\]
\[=\dfrac{4}{3}\times \dfrac{22}{7}\times {{\left( 4.2 \right)}^{3}}\]
\[\begin{align}
  & =\dfrac{4}{3}\times \dfrac{22}{7}\times 4.2\times 4.2\times 4.2 \\
 & =4\times 22\times 0.6\times 1.4\times 4.2 \\
 & =310.464c{{m}^{3}} \\
\end{align}\]
Hence, we got the volume of the sphere- shaped metallic shot put as \[310.464c{{m}^{3}}\].

Note: Read the question to find if radius or diameter is given. If it’s the radius then we can directly use the formula of volume. If diameter is given, either change it to radius or change the formula by substituting, \[r=\dfrac{d}{2}\].
\[\dfrac{4}{3}\pi {{r}^{3}}=\dfrac{4}{3}\pi {{\left( \dfrac{d}{2} \right)}^{3}}=\dfrac{4}{3}\pi \times \dfrac{{{d}^{3}}}{8}=\dfrac{\pi {{d}^{3}}}{6}\]