Question

The ratio of height to the base radius of a cone is 3:4. If the volume of the cone is 2000πcm³, find its radium, in cm.

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Answer 1

20 cm

Explanation:

The volume, V, of a cone with radius r and height h is given by the formula

V =
`(1/3) \pi r^2 h`

Since it is given that the ratio of h to r is 3/4 we have the relationship

h/r = 3/4 ==> h = (3/4)r

Substituting for h in the volume equation gives us an expression in terms of r

`(1/3)\pir^2h = (1/3) \pi r^2 (3/4)r\\(1/3 ) (3/4) = 1/4\\`

So the expression simplifies to
`(1/4)\pi r^3`

We are given that this volume is 2000π cm³

So

(1/4)πr³ = 2000π

Eliminating π on both sides and multiplying by 4 on both sides gives

r³ = 8000

r = ∛8000 = 20 cm Answer