Height of a right circular cylinder is twice of its radius. If the height would be 6 times of its radius, then the volume of the cylinder would be greater by 4312 cubic.dcm. Calculate the radius of the cylinder.

Explanation

Let the radius of the cylinder be r dcm.
`:.` height `= 2 r ` dcm
`:.` volume `= (22)/(7) xx r^(2) xx 2r` cubic.dcm`=(44)/(7) r^(3)` cubic.dcm.
If the height be 6 times of its radius, i.e., if h = 6 r , then volume
`= (22)/(7) xx r^(2) xx 6r` cubic. dcm `= (132 r^(3))/(7) ` cubic.dcm
As per question, `(132 r^(3))/(7) - (44)/(7) r^(3)= 4312`
or, `(88 r^(3))/(7) = 4312` or, `r^(3)= (4312xx7)/(88)` or, `r^(3) = 49 xx 7 = 7^(3) ` or, `r = 7 `
Hence the required radius = 7 dcm.
Hence the required radius = 7 dcm.