Multiple choice

A solid is in the shape of a cylinder surmounted on a hemisphere. If the diameter and the total height of the solid are $21cm,25.5cm$ respectively, then find its volume.

  1. $7623{cm}^{3}$
  2. $723{cm}^{3}$
  3. $763{cm}^{3}$

  4. None of these
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A Correct answer
Explanation

The solid consists of a hemisphere (radius 10.5 cm) and a cylinder (radius 10.5 cm, height 25.5 - 10.5 = 15 cm). Volume = (2/3) * pi * r^3 + pi * r^2 * h. Using pi = 22/7, Volume = (2/3)(22/7)(10.5)^3 + (22/7)*(10.5)^2 * 15 = 2425.5 + 5197.5 = 7623 cm^3.

AI explanation

The common radius is r = 21/2 = 10.5 cm, and the height of the cylindrical part is 25.5 - 10.5 = 15 cm. The total volume is the sum of the cylindrical volume and the hemispherical volume, calculated as π * 10.5^2 * 15 + (2/3) * π * 10.5^3. Using π = 22/7, this evaluates to 5197.5 + 2425.5 = 7623 cm^3. The result is 7623 cm^3.

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