Multiple choice

A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm2) in the total surface area?

  1. 77

  2. 154

  3. 87

  4. 38.5
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A Correct answer
Explanation

Cutting a sphere into two halves creates two new circular faces, each with area pi * r^2. The diameter is 7 cm, so the radius r is 3.5 cm. The increase in surface area is 2 * pi * (3.5)^2 = 2 * (22/7) * 12.25 = 77.

AI explanation

When a sphere of radius 3.5 cm is cut into two equal halves, the increase in the total surface area equals the combined area of the two newly exposed flat circular faces. This increase is calculated as 2 * π * r^2, which is 2 * (22/7) * (3.5)^2 = 77 cm2.

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