d If the volume and surface area of a sphere JEMrare.com

# Volumes MCQ 1: If the volume and surface area of a sphere are numerically the same, then its radius is…….?

a) 1 unit                 b) 2 units                        c) 3 units                   d) 4 units

Solution:

In this problem the 3D shape of which area and volume is discussed – is a round  sphere !

We should know the formulas for surface area and volume of a sphere if radius is given.

If radius of a sphere be “r” then;

$Volume = \frac{4 }{3}\pi r^3$

and

$Surface Area=4\pi r^2$

Since it is given that volume and surface area are equal to each other – (as per question statement )i-e

$4\pi r^2 =\frac{4}{3}\pi r^3$

from which after calculation we have,

$3 =r$

i-e its radius is 3 units !

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