Discussion

The volume of a cone whose base diameter is 7 cm and whose height is 14 cm is

Answer: C

Halve the diameter to get the base radius, then use the cone volume formula with \( \pi = \tfrac{22}{7} \).

\[ r = \frac{7}{2} = 3.5 \text{ cm}, \qquad h = 14 \text{ cm} \]

\[ V = \frac{1}{3}\pi r^{2} h = \frac{1}{3} \times \frac{22}{7} \times (3.5)^{2} \times 14 \]

\[ = \frac{1}{3} \times \frac{22}{7} \times 12.25 \times 14 = \frac{1}{3} \times 539 \]

\[ V \approx 180 \text{ cm}^{3} \]

Forgetting the \( \tfrac{1}{3} \) would give the volume of the enclosing cylinder, three times too large.

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