Question

the radii of two cones are in the ratio 2:1 and the volume are equal . what is ratio their heights

Answer 1

Let the radii of the two cones be 2x and x. Their heights are h1 and h2.

We know that volume of the cone = 1/3pir^2h.

1/3 * pi * (2x)^2 * h1 = 1/3 * pi * (x)^2 * h2

h1/h2 = 1/4.

Therefore the ratio of their heights = 1: 4.


Hope this helps! 

Answer 2

Answer:

Step-by-step explanation:

Let their radii be 2x, x and their heights be h and H resp.

Then,

Volume of cone =1/3πr^2h

={(1/3πr^2h)/(1/3πr^2H)}

={(1/3π(2x)^2h)/(1/3π xH)}

=h/H=1/4

so h:H=1:4