Discussion
If a right circular cone hs radius 4 cm and slant height 5 cm then what is its volume?
Answer: A
Volume needs the perpendicular height, not the slant height, so find it by Pythagoras first.
\[ h = \sqrt{l^{2} - r^{2}} = \sqrt{5^{2} - 4^{2}} = \sqrt{9} = 3 \text{ cm} \]
\[ V = \frac{1}{3}\pi r^{2} h = \frac{1}{3}\pi (4)^{2}(3) = \frac{1}{3}\pi (16)(3) = 16\pi \text{ cm}^{3} \]
Using the slant height of 5 in place of \( h \) would give \( \tfrac{80}{3}\pi \) - the standard slip in every cone question that supplies \( l \) rather than \( h \).
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