Question

Find the volume of sphere whose area is 154 cm2

Answer 1

Hint: The Area of the sphere is given, it can be used to calculate the value of r which can then be substituted in the formula of volume to find the required value.
For a sphere, we have:
\[SurfaceArea = 4\pi {r^3}\]
\[Volume = \dfrac{4}{3}\pi {r^3}\]

Complete step-by-step answer:

We have,
Surface Area of sphere =154 cm2 (Given)
Therefore,
$4\pi {r^2} = 154$ (SA of sphere =\[4\pi {r^2}\])
Calculating for r:
${r^2} = \dfrac{{154}}{{4\pi }}$
${r^2} = \dfrac{{154 \times 7}}{{4 \times 22}}$
${r^2} = 12.25$

Square rooting both sides, we have:
$\sqrt {{r^2}} = \sqrt {12.25} $
$r = 3.5cm$
Volume of sphere: \[ = \dfrac{4}{3}\pi {r^3}\]
Substituting value of r, we get:

\[\dfrac{4}{3}\pi {r^3} = \dfrac{4}{3} \times \dfrac{{22}}{7} \times {\left( {3.5} \right)^3}c{m^3}\]
\[ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times 3.5 \times 3.5 \times 3.5c{m^3}\]
\[ = \dfrac{4}{3} \times \dfrac{{22}}{7} \times \dfrac{{35}}{{10}} \times \dfrac{{35}}{{10}} \times \dfrac{{35}}{{10}}c{m^3}\]
\[ = \dfrac{2}{3} \times 22 \times 1 \times \dfrac{{35}}{{10}} \times \dfrac{{35}}{{10}}c{m^3}\]
$ = \dfrac{{53900}}{{300}}$
$ = 179.66c{m^3}$
Therefore the volume of the sphere whose surface area is 154 cm2 is 179.66 cm3.

Note: In such questions where value of one entity is given and other needs to be found, we look out for the common variable among the two, calculate its value from the given entity and substitute in the unknown so as to get the desired results.
Try removing decimals so as to make the calculation easier and calculate square root by pairing method (as shown).