Multiple choice

A lead pencil is in the shape of a cylinder. The pencil is $21 cm$ long with radius $0.4 cm$ and its lead is of radius $0.1 cm$. What is the volume of wood in the pencil?

  1. $9.9 cm^{3}$
  2. $8.9cm^3$
  3. $7.8 cm^3$
  4. $8.5 cm^3$
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A Correct answer
Explanation

The volume of wood is the volume of the cylinder with radius 0.4 cm minus the volume of the lead cylinder with radius 0.1 cm. Volume = pi * h * (R^2 - r^2) = (22/7) * 21 * (0.4^2 - 0.1^2) = 66 * (0.16 - 0.01) = 66 * 0.15 = 9.9 cubic cm.

AI explanation

The volume of a cylinder is found using the formula pi * r^2 * h. The volume of the wood is the difference between the volume of the entire pencil and the volume of its lead, calculated as pi * h * (R^2 - r^2). Substituting the given values gives a volume of (22/7) * 21 * ((0.4)^2 - (0.1)^2), which simplifies to 66 * (0.16 - 0.01) cubic centimeters. This results in a wood volume of 9.9 cm^3.

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