Multiple choice

The radius of a sphere is 2 cm. If an error of 0.02 cm is made in measuring the radius of the sphere, find the percentage error in measuring its surface area.

  1. ±3%

  2. ±2%

  3. ±1%

  4. ±5%
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B Correct answer
Explanation

The surface area of a sphere is S = 4 * pi * r^2. Differentiating, dS = 8 * pi * r * dr. The relative error is dS/S = (8 * pi * r * dr) / (4 * pi * r^2) = 2 * (dr/r). Given r = 2 and dr = 0.02, the relative error is 2 * (0.02 / 2) = 0.02, which is 2%.

AI explanation

The surface area of a sphere is proportional to the square of its radius. The percentage error in the radius is 0.02 divided by 2, multiplied by 100, which equals 1 percent. Because the area depends on the square of the radius, the percentage error in the surface area is 2 percent. The result is an error of plus or minus 2 percent.

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