Question

(a)
The ratio of volumes of two cones is 2:3 and the ratio of the radii of their base is 1:2, then
the ratio of their heights is
(a) 3:8
(b) 8:3
(c) 3:4
(d) 4:3
Ae
JOT
AB
4​

Answer 1

Answer:

The ratio of their height is 8 : 3

Explanation:

Let, the volume of the first cone= 2v, and second cone = 3v

Base radius of first cone= r, base radius of second cone = 2r

Let, first cone's height = x and second cone's height = y

ATP,

$\frac{ \frac{\pi \times {r }^{2} \times x}{3} }{ \frac{\pi \times ( {2r)}^{2} \times y}{3} } = \frac{2v}{3v}$

$\frac{ {r}^{2} \times x}{4 {r}^{2} \times y} = \frac{2}{3}$

$\frac{x}{y} = \frac{2 \times 4}{3 \times 1}$

$\frac{x}{y} = \frac{8}{3}$

x : y = 8 : 3