Question

Choose the correct answer in each of the following :

If the volumes of two cones be in the ratio 1:4 and the radii of their bases be in the ratio 4:5 then ratio of their heights is

(a) 1:5 (b) 5:4 (c) 25:16 (d) 25:64

Answer 1

ans-d
Here, given Volume of the two cones = 1 :4

and diameter = 4 : 5

then , find ratio of height ???

now,
the solution:-

($\frac{1}{3}\pi r_1^2{h}_1$) / ( $\frac{1}{3}\pi r_2^2{h}_2$) = $\frac{1}{4}$.............【1】

$\frac{d1}{d2}=\frac{2r1}{2r2}=\frac{4}{5}$........................【2】

now, by simplifying eqn 【1】as

( r1 /r2 )² h1 /h2 = 1/ 4

now, similarly by using eqn【2】we get the result,

( 4/5 )² × h1 / h2 = 1/ 4
so, h1 / h2 = 1 /4 × 25/ 16
therefore, h1/ h2 = 25 / 64

therefore , we can say ratio of their heights = 25 : 64