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?

1 Answer
Aug 27, 2017

Answer:

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]