Question

If the ratio of the volume of two circular cone is 1:4 and the ratio of radii of their bases is 4:5 then the ratio of the height is

Answer 1

The ratio of the height 25 : 64

Explanation:

Answer 2

`(125)/(64)`

Step-by-step explanation:

First, we have to understand how to solve for volume of a cone. The formula is:
`V = (1)/(3) \pi r^2h` . In this question we know that
`V_(1)` :
`V_(2)` = 1:4, and
`r_(1)` :
`r_(2)` = 4:5. We can apply the volume formula now:
`4 *(1)/(3) \pi r_1^2h_1 = 5 * (1)/(3) \pi r_2^2h_2`. Substituting the values of
`r_(1)` and
`r_(2)` into the above equation gets us
`(64)/(3) \pi h_1 = (125)/(3) \pi h_2` . If we continue to simplify this, we get
`(h_(1))/(h_(2)) = (125)/(64)`, which is our final answer.