Multiple choice

If a solid right circular cylinder, made of iron is heated to increase its radius and height by $1 \%$ each, then by how much percent is the volume of the solid increased?

  1. $3.03\%$
  2. $3.5\%$
  3. $4\%$
  4. $2.5\%$
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A Correct answer
Explanation

Volume V = pi * r^2 * h. If r and h increase by 1%, the new volume V' = pi * (1.01r)^2 * (1.01h) = pi * r^2 * h * (1.01)^3. (1.01)^3 = 1.030301. The increase is 3.03%.

AI explanation

The volume of a right circular cylinder is given by the formula V = pi * r^2 * h. Using the successive percentage change formula for dependent variables, the net percentage increase in volume is calculated as a + b + c + (ab + bc + ca)/100 + abc/10000. Substituting the 1 percent increases for radius (twice) and height, we get 1 + 1 + 1 + (1 + 1 + 1)/100 + 1/10000, which equals 3.03 percent. The percentage increase in the volume is 3.03%.

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