The ratio of the volumes of a cylinder and a sphere is 1 : 3 and the ratio of the radii of the base of the cylinder and of the sphere is 1: 3 and If the sum of the height and radius of base of the cylinder is 78 cm , then what will be the height of the cylinder ?

Explanation

Let the radii of the cylinder and the sphere be x cm and 3x cm respectively . Also let the volumes of the cylinder and the sphere be V and 3 V respectively .
As per question ` x+ h = 78 . . . . . . . . . . . ` (1)
Again , `V = pix^(2) h ` cu - unit and `3V = 4/3 pi xx (3x)^(3)` cu - unit
` rArr 3pi r^(2) h = 36 pix^(3) rArr h = (36x^(3))/(3x^(2)) = 12 x `
` :. ` from (1) we get , `12 x + x = 78`
or , 13 x = 78 or, x = `78/13` = 6
and h = 12 x `rArr h = 12 xx 6 = 72`
Hence the height of the cylinder = 72 cm