Multiple choice

The volume of a solid in the form of a cylinder with hemispherical ends whose extreme length is 23 cm and radius 3 cm is

  1. 594 $ \displaystyle cm^{3} $
  2. 694 $ \displaystyle cm^{3} $
  3. 794 $ \displaystyle cm^{3} $
  4. 894 $ \displaystyle cm^{3} $
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A Correct answer
Explanation

The solid consists of a cylinder of length (23 - 3 - 3) = 17 cm and two hemispheres of radius 3 cm. Volume = pi * r^2 * h_cyl + (4/3) * pi * r^3 = pi * 3^2 * 17 + (4/3) * pi * 3^3 = 153 * pi + 36 * pi = 189 * pi. Using pi approx 3.14, 189 * 3.14 = 593.46, which is approximately 594.

AI explanation

The extreme length of 23 cm includes the cylinder length and two hemispherical radii, making the cylinder height 23 - 2(3) = 17 cm. The volume of the solid is the sum of the cylinder volume and the volumes of the two hemispheres, which form one full sphere of radius 3 cm. Using the formulas, the total volume is pi * 3^2 * 17 + (4/3) * pi * 3^3 = 153pi + 36pi = 189pi. Using pi as 22/7, the volume is 189 * 22/7 = 27 * 22 = 594 cubic cm.

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