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Question
A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which the water will rise in the cylinder.
Solution
Given that
Volume of water in the hemisphere bowl = Volume of water in the cylinder
Let n be the height to which water rises in the cylinder.
Inner radii of bowl =3.5cm= `r_1`
Inner radii of bowl = 7cm=`r_2`
⇒ `2/3πr_1^3=πr_2^2h`
⇒ h= `(2r_1^3)/(3r_2^2)=(2(3.5)^3)/(3(7)^2)`
⇒ `h =7/12cm.`
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