Question

If the radius of the sphere is 3r, then what is its volume?

Answer 1

Hint: Apply the formula for volume of a sphere which is \[V = 4\pi {R^3}\]. Using this find the volume of the sphere as described in the question.

Complete step-by-step answer:
We know that the formula for volume of a sphere is \[V = 4\pi {R^3}\] where V is the volume R is the radius of the sphere and \[4\pi \] is the constant part.
Now according to the question it is given that
\[R = 3r\] where r is a given constant and R is the radius.
Putting this in place of radius we get it as
\[\begin{array}{l}
\therefore V = 4\pi {R^3}\\
 \Rightarrow V = 4\pi {(3r)^3}\\
 \Rightarrow V = 4\pi {(3)^3} \times {(r)^3}\\
 \Rightarrow V = 4\pi \times 27 \times {r^3}\\
 \Rightarrow V = 108\pi r{}^3
\end{array}\]
So from here we are getting the volume as \[108\pi r{}^3\]

Note: Changing the value of radius in the formula was the essential and only part because many students confuse r with the radius i.e., R and forget to change the value.