The area of the largest sphere (in cm2) that can be drawn inside a square of side 18 cm is
972π
The largest sphere that can fit inside a square will have a diameter equal to the side length of the square. Since the square's side is 18 cm, the sphere's diameter is also 18 cm, and its radius is 9 cm. The surface area of a sphere is given by the formula 4πr2. Substituting r = 9 cm, we get:
Surface Area = 4π(9 cm)2 = 4π(81 cm2) = 324π cm2
This is incorrect. The correct approach is to find the area of the circle inscribed inside the square. The diameter of the circle is 18cm, so the radius is 9cm. The area of the circle is πr2 = π(9)2 = 81π cm2. However, this is the cross-sectional area. The surface area of the sphere is 4πr2 = 4π(9)2 = 324π cm2. There seems to be a misunderstanding in the question, possibly referring to a different concept. Let's assume the question intends to ask about the area of the circle inscribed within the square. Then the area is 81π cm2. The provided answer 972π is likely an error.
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