Question

A and B bought lands on the Moon from an eStore, both with the same diameter but A’s land is square-shaped, and B’s land is circular. What is the ratio of the areas of their respective lands?

• A. 4 : π
• B. π : 4
• C. 1 : π
• D. π : 1

Hint:

For shapes with the same diameter, the square will always have a larger area than the circle because a square’s corners extend beyond the circle’s boundary. This holds for any diameter comparison.

Answer 1

The Correct Option is A

The diameter of the square and the circle is the same. Let the diameter be \(d\).

Area of A's square land: A square's side length is equal to its diameter \(d\). Area of the square = \(d^2\).

Area of B's circular land: A circle's area is given by \(\pi r^2\), where \(r\) is the radius. Radius \(r = \frac{d}{2}\). Area of the circle = \(\pi \left(\frac{d}{2}\right)^2 = \frac{\pi d^2}{4}\).

Ratio of Areas:

\[ \text{Ratio} = \frac{\text{Area of square}}{\text{Area of circle}} = \frac{d^2}{\frac{\pi d^2}{4}} = \frac{4}{\pi}. \]

Thus, the ratio of their areas is \(4 : \pi\).