Question

The height of a circular cylinder of given volume varies inversely as the square of the radius of the base. How many times greater is the radius of a cylinder 3 m high than the radius of a cylinder 6 m high with the same volume?

Answer 1

The radius of cylinder of `3` m high is `sqrt2` times greater
than that of `6m` high cylinder.

Explanation:

Let `h_1=3` m be the height and `r_1` be the radius of the 1st cylinder.

Let `h_2=6`m be the height and `r_2` be the radius of the 2nd cylinder.

Volume of the cylinders are same .

`h prop 1/r^2 :. h = k*1/r^2 or h *r^2 = k :. h_1*r_1^2= h_2*r_2^2`

`3 * r_1^2 = 6*r_2^2 or (r_1/r_2)^2 =2 or r_1 /r_2= sqrt2` or

`r_1= sqrt2*r_2`

The radius of cylinder of `3` m high is `sqrt2` times greater

than that of `6m` high cylinder [Ans]