Multiple choice

A toy consists of a cone surmounted by a hemisphere. The cone has a radius of 8 centimeters and a height of 15 centimeters. The hemisphere has the same radius as the cone. What is the approximate volume of the toy?

  1. 341.33π cubic centimeters

  2. 541.33π cubic centimeters

  3. 661.33π cubic centimeters

  4. 681.33π cubic centimeters
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C Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * 64 * 15 = 320 * pi. Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * pi * 512 = 341.33 * pi. Total volume = 320 * pi + 341.33 * pi = 661.33 * pi.

AI explanation

The total volume of the toy is the sum of the volume of the cone and the hemisphere, using the formulas 1/3 pi radius squared height and 2/3 pi radius cubed. Substituting the given radius of 8 and height of 15 gives the equation total volume equals 1/3 pi times 64 times 15 plus 2/3 pi times 512. This simplifies to 320 pi plus 1024/3 pi, which equals 1984/3 pi cubic centimeters. Converting this to a decimal yields approximately 661.33 pi cubic centimeters.

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