Two right circular cones of equal volumes have their heights in the ratio 4 : 9. What is the ratio of the radii of their bases, the cones coming in the same order as that in which the ratio of their heights is given?
Answer & explanation
Correct answer: option 2
We know that,
Volume of a cone = \(\frac{1}{3}\)πr2h
Ratio of the heights of the cones = 4 ∶ 9.
Let the radius of the two cones = m and n
Also, let the heights of the cones be 4a and 9a
According to the question,
\(\frac{1}{3}\)π × m2 × 4a = \(\frac{1}{3}\)π × n2 × 9a
= 4m2 = 9n2
= \(\frac{m}{n}\) = \(\frac{3}{2}\)
Ratio of radii = 3 : 2