Multiple choice

A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is $10$ cm, and its base is of radius $3.5$ cm, find the volume of wood in the toy. $\displaystyle \left[ Use \,\,\, \pi = \frac{22}{7} \right]$

  1. $425$
  2. $290$
  3. $474.83$
  4. $205.33$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = (22/7) * 3.5^2 * 10 = 22 * 0.5 * 3.5 * 10 = 385. Volume of two hemispheres = 2 * (2/3) * pi * r^3 = (4/3) * (22/7) * 3.5^3 = (4/3) * (22/7) * 42.875 = 179.66. Volume of wood = 385 - 179.66 = 205.33.

AI explanation

The radius of the cylinder and both hemispheres is 3.5 cm, meaning the total height of 10 cm is composed of the two hemispherical radii and the remaining cylinder height. The remaining cylinder height is 10 minus 3.5 minus 3.5, which is 3 cm. The volume of the wood is the volume of this remaining cylinder plus the volume of both hemispheres, calculated as pi times 3.5 squared times 3 plus two times two thirds times pi times 3.5 cubed, yielding 205.33 cubic centimeters.

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