Multiple choice

A toy is in the shape of hemisphere mounted on a cone such that the radius of hemisphere is 21 cm. If the volume of the toy is 24024 cm3, then find the height of conical part of toy.

  1. 15 cm

  2. 12 cm

  3. 10 cm

  4. 22 cm

  5. 18 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * (22/7) * 21^3 = 19404. Volume of cone = 24024 - 19404 = 4620. Volume of cone = (1/3) * pi * r^2 * h = (1/3) * (22/7) * 21^2 * h = 462 * h. So 462 * h = 4620, h = 10 cm.

AI explanation

The volume of the hemisphere is (2/3) * (22/7) * 21^3 = 19404 cm3. The volume of the conical part is the total volume minus the hemisphere's volume, 24024 - 19404 = 4620 cm3. Using the cone volume formula, (1/3) * (22/7) * 21^2 * h = 4620, which simplifies to 462h = 4620. The height of the conical part is 10 cm.

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