Volumes MCQ 1: ( If the volume and surface area of a sphere )
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.
\[ Volume = \frac{4 }{3}\pi r^3 \]
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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