Question : The side of a square is equal to 40% of the radius of a sphere. If the volume of the sphere is $\frac{500 \pi}{3} \mathrm{~m}^3$, then what is the area of the square?
Option 1: 2 m2
Option 2: 1 m2
Option 3: 9 m2
Option 4: 4 m2
Correct Answer: 4 m 2
Solution :
The Volume of a sphere is $\frac{500\pi}{3}$ m$^3$.
Side of square = 40% radius of the sphere
Area of square = Side$^2$
According to the question,
The volume of a sphere = $\frac{4}{3}\pi r^3$
⇒ $\frac{4}{3}\pi r^3$ = $\frac{500\pi}{3}$
⇒ $r^3$ = $\frac{500}{4}$
⇒ $r^3$ = 125
⇒ $r$ = 5 m
Side of square = $\frac{40}{100} \times 5$ = 2 m
Area of square = Side$^2$
= 2$^2$ = 4 m
2
$\therefore$ Area of the square is 4 m$^2$.
Hence, the correct answer is 4 m$^2$.
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