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Volumes MCQ 1: ( Sphere, surface area, volume)

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 sphere !

We should know the formulas for surface area and volume of a sphere.drawit diagram 1

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 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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