Geometry and TrigonometryEasy–MediumHeight of a cone from its volume
Geometry and Trigonometry practice question
A cone has a volume of 12π cubic units and a base radius of 3 units. What is its height, in units?
Answer: 4
V = (1/3)πr²h: 12π = (1/3)π(9)h = 3πh, so h = 4.
Common wrong answers
- If you answered 12
- 12 divides 12π by π alone, ignoring both the 1/3 and the r² = 9.
- If you answered 36
- 36 multiplies 12 by 3 without dividing by r² = 9.
- If you answered 1.33
- 1.33 forgets the 1/3: 12π = 9πh gives h = 4/3.
More Geometry and Trigonometry questions
- Easy–Medium
A circle has a radius of 6. What is its area? (Use A = πr².) - Easy–Medium
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse? - Easy–Medium
A circle has a radius of 5. What is its circumference? (Use C = 2πr.) - Easy–Medium
What is the midpoint of the segment joining the points (2, 3) and (8, 11)? - Easy–Medium
What is the measure, in degrees, of angle B? - Easy–Medium
What is the area, in square centimeters, of the trapezoid?
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