Practice | Hashtable

1. If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their height will be :

A. 3 : 4

B. 4 : 3

C. 3 : 8

D. 8 : 3

Solution:

let their radii be x and 2x, and their heights be h and H respectively
Then,

\begin{aligned} \frac{\frac{1}{3} \times π \times x^{2} \times h}{\frac{1}{3} \times π \times {(2 x)}^{2} \times H} = \frac{2}{3} \\ \Leftrightarrow \frac{h}{H} = \frac{2}{3} \times 4 \\ \Leftrightarrow \frac{h}{H} = \frac{8}{3} O r 8 : 3 \end{aligned}

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