Geometry and TrigonometryHardRadius of a cone from its volume
Geometry and Trigonometry practice question
A cone has a volume of 12π cubic centimetres and a height of 4 centimetres. What is the radius of its base, in centimetres? (The volume of a cone is (1/3)πr²h.)
Answer: 3
(1/3)πr²(4) = 12π gives (4/3)r² = 12, so r² = 9 and r = 3.
Common wrong answers
- If you answered 1
- 1 comes from r² = 12/12, forgetting the factor 4/3 from the height and the 1/3.
- If you answered 9
- 9 is r²; take the square root.
- If you answered 36
- 36 is r² without dividing by the 4/3, or 9 × 4.
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