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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`
Solution
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
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