Multiple choice

A cone of height 12 cm and diameter 10 cm is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed?

  1. 384.13 cm3

  2. 576.19 cm3

  3. 192.06 cm3

  4. 288.1 cm3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Radius r = 5 cm, height h = 12 cm. Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * 25 * 12 = 100 * pi. Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * pi * 125 = 83.33 * pi. Total volume = 183.33 * pi = 575.96. 576.19 is the closest approximation.

AI explanation

The common diameter is 10 cm, so the radius r is 5 cm. The volume of the cone is one third times pi times r squared times height, which is one third times pi times 25 times 12, equaling 314.16 cm3. The volume of the hemisphere is two thirds times pi times r cubed, which is two thirds times pi times 125, equaling 261.8 cm3. Adding these two volumes gives a total volume of 576.19 cm3.

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