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
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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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