Multiple choice

A cone of height 16 cm and diameter 14 cm is mounted on a hemisphere of same diameter. What is the volume of the solid thus formed? (Take π = 22 7 )

  1. 1,540 cm3

  2. 1,078 cm3

  3. 1,048 cm3

  4. 770 cm3
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A Correct answer
Explanation

Volume = Volume of cone (1/3 * pi * r^2 * h) + Volume of hemisphere (2/3 * pi * r^3). With r = 7 and h = 16: V = (1/3 * 22/7 * 49 * 16) + (2/3 * 22/7 * 343) = (22 * 7 * 16 / 3) + (44 * 49 / 3) = 2464/3 + 2156/3 = 4620/3 = 1540.

AI explanation

The volume of the solid is the sum of the volume of the cone and the volume of the hemisphere. The cone has a radius of 7 cm and a height of 16 cm, so its volume is (1/3)π(7²)(16) = (784/3)π cm³. The hemisphere has a radius of 7 cm, giving a volume of (2/3)π(7³) = (686/3)π cm³. Adding these gives a total volume of (1470/3)π = 490π cm³, and using π = 22/7 results in 490 * (22/7) = 1540 cm³.

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