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Mathematics

A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively 6 cm and 4 cm. Find the height of water in the cylinder.

Mensuration

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Answer

Radius of hemispherical bowl (r) = 6 cm.

Radius of cylinder (R) = 4 cm.

Let h be the height of water in cylinder.

Volume of hemispherical bowl = Volume of water in cylinder.

⇒23πr3=πR2h⇒23r3=R2h⇒23×63=42×h⇒2×2×36=16h⇒h=14416⇒h=9 cm.\Rightarrow \dfrac{2}{3}πr^3 = πR^2h \\[1em] \Rightarrow \dfrac{2}{3}r^3 = R^2h \\[1em] \Rightarrow \dfrac{2}{3} \times 6^3 = 4^2 \times h \\[1em] \Rightarrow 2 \times 2 \times 36 = 16h \\[1em] \Rightarrow h = \dfrac{144}{16} \\[1em] \Rightarrow h = 9 \text{ cm}.

Hence, the height of water in cylinder is 9 cm.

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