Question

Oil is stored in a spherical vessel occupying `3/4` of its full capacity. Radius of this spherical vessel is 28 cm. This oil is then poured into a cylindrical vessel with a radius of 21 cm. Find the height of the oil in the cylindrical vessel (correct to the nearest cm). Take π = `22/7`

Answer 1

Radius of spherical vessel, R = 28 cm

Radius of cylindrical vessel, r = 21 cm

Let, the height of cylindrical vessel be h cm

Volume of oil in sphere = `3/4 xx 4/3 πR^3`

= `22/7 xx 28 xx 28 xx 28`

Then, volume of oil in cylindrical vessel = Volume of oil in spherical vessel

`\implies π xx r^2h = 22/7 xx 28 xx 28 xx 28`

`\implies 22/7 xx 21 xx 21 xx h = 22/7 xx 28 xx 28 xx 28`

`\implies h = (28 xx 28 xx 28)/(21 xx 21)`

= `(4 xx 4 xx 28)/(3 xx 3)`

= 49.78 cm