Multiple choice

A lead pencil is in the shape of right circular cylinder. The pencil is $28cm$ long and its radius is $3mm$. If the lead is of radius $1mm$, then find the volume of the wood used in the pencil.

  1. $7.04{cm}^{3}$
  2. $7.14{cm}^{3}$
  3. $8.04{cm}^{3}$

  4. None of these
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A Correct answer
Explanation

The volume of the wood is the volume of the cylinder minus the volume of the lead core. Volume = pi * (R^2 - r^2) * h. With R = 0.3 cm, r = 0.1 cm, and h = 28 cm, Volume = pi * (0.09 - 0.01) * 28 = pi * 0.08 * 28 = 2.24 * 3.14159 = 7.037 cm^3, which rounds to 7.04 cm^3.

AI explanation

First convert the measurements to centimeters so the radius of the pencil is 0.3 cm, the radius of the lead is 0.1 cm, and the height is 28 cm. Using the volume of a cylinder formula V = pi * (R^2 - r^2) * h, the volume of the wood is pi * (0.3^2 - 0.1^2) * 28. This simplifies to 22/7 * (0.09 - 0.01) * 28, which equals 22 * 0.08 * 4, resulting in 7.04 cm^3.

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