The area of a circle is 40π2. The area of a square with sides equal to radius…
2023
The area of a circle is 40π2. The area of a square with sides equal to radius of the circle is
Answer: C. 40π — ConceptFor a circle of radius r, the area is πr2. For a square of side s, the area is s2. When the square's side equals the circle's radius, s = r, so the…
- A.
4π
- B.
4π2
- C.
40π
- D.
More than one of the above
- E.
None of the above
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Correct answer: C
Concept
For a circle of radius r, the area is πr2. For a square of side s, the area is s2.
When the square's side equals the circle's radius, s = r, so the square's area is r2.
Application
Let r be the circle's radius. The given area gives πr2 = 40π2.
Divide both sides by π: r2 = 40π.
The square has side r, so its area is r2 = 40π square units.
Cross-check
Substituting r2 = 40π into the circle formula gives πr2 = π(40π) = 40π2, which reproduces the given area.
Therefore, the area of the square is 40π square units.