Question

24. A spherical balloon with a surface area of 36π square inches is inflated further until its diameter has increased by 50%. The surface area of the balloon is now: A. 54π square inches. B. 81π square inches. C. 122π square inches. D. 216π square inches.

Answer 1

The surface area of a sphere is calculated by the formula A=4πr². Given the initial surface area and a 50% increase in the sphere's diameter, the new surface area is 81π square inches.

Step-by-step explanation:

The subject of this question is Mathematics and is likely at a high school level. The problem is about understanding the relationship between the radius (or diameter) and the surface area of a sphere. The surface area (A) of a sphere can be computed using the formula A=4πr², where r is the radius of the sphere. Initially, we have A1=4πr₁²=36π which gives us r₁=3. When the diameter (and thus the radius r₂) increases by 50%, r₂ becomes 1.5 * r₁, which is 4.5. The new surface area, A2, can be computed using the formula A=4πr₂². Plugging in our values, A2=4π * (4.5)²=81π square inches. So the correct answer is B. 81π square inches.

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