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प्रश्न
A solid is in the shape of a hemisphere of radius 7 cm, surmounted by a cone of height 4 cm. The solid is immersed completely in a cylindrical container filled with water to a certain height. If the radius of the cylinder is 14 cm, find the rise in the water level.
उत्तर
Volume of solid = `1/3πr^2h + 2/3πr^3`
= `1/3πr^2 (h + 2r)`
= `π/3 xx (7)^2 xx (4 + 2 xx 7)`
= `π/3 xx 49 xx 18`
= 294π cm3
Let y be the height rise of water in a cylindrical cylinder with radius R = 14 cm.
∴ Volume of water rise in a cylindrical container = Volume of solid immersed
πR2y = 294π
`\implies` π(14)2y = 294π
∴ y = `294/(14 xx 14)`
= `21/14`
= `3/2`
= 1.5 cm
Hence, The rise in the water level is y = 1.5 cm
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