Discussion
The curved surface area of a right circular cone is 444 \(\pi\) cm3 and the diameter of its base is 24 cm. What is the volume of the cone (in cm3)?
Answer: D
The volume of the cone is \(1680\pi\) cm3. The base radius is 12 cm. The curved surface area is \(\pi r l\), so \[ \begin{aligned} \pi\times 12\times l &= 444\pi \Rightarrow l \\ &= 37\text{ cm} \end{aligned} \] The height follows from the right triangle: \[ \begin{aligned} h &= \sqrt{37^{2} - 12^{2}} \\ &= \sqrt{1369 - 144} \\ &= \sqrt{1225} \\ &= 35 \end{aligned} \] \[ \begin{aligned} V &= \frac{1}{3}\pi r^{2}h \\ &= \frac{1}{3}\pi\times 144\times 35 \\ &= 1680\pi \end{aligned} \] The options 840, 1120 and 1400 times \(\pi\) correspond to heights of 17.5, 23.3 and 29.2, which do not fit a slant height of 37.
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