Question : A cone and a cylinder with equal radii have equal volumes. The ratio of their heights is:
Option 1: 2 : 3
Option 2: 3 : 4
Option 3: 1 : 2
Option 4: 3 : 1
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Correct Answer: 3 : 1
Solution :
Let radius of cylinder = radius of cone = $r$
Volume of cylinder = $\pi r^2 h_1$
Volume of cone = $\frac{\pi r^2 h_2}3$
When the radius and volume are the same,
${(\pi r^2 h_1)}={(\frac{\pi r^2h_2}3)}$
⇒ $\frac{h_2}{h_1}$ = 3 : 1
Hence, the correct answer is 3 : 1.
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