A vessel full of water is in the form of an inverted cone of height 8 cm and the radius of its top, which is open, is 5 cm. 100 spherical lead balls are dropped into the vessel. One fourth of the water flows out of the vessel. Find the radius of a spheric

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Solution

Q.
A vessel full of water is in the form of an inverted cone of height 8 cm and the radius of its top, which is open, is 5 cm. 100 spherical lead balls are dropped into the vessel. One fourth of the water flows out of the vessel. Find the radius of a spherical ball.

Ans.
(0.5)

Height (h) of the cone = 8 cm and radius (r) of the cone = 5 cm

$∴$ Volume of water flows out $= \frac{1}{4} \times$ volume of cone

$= \frac{1}{4} \times \frac{1}{3} π r^{2} h = \frac{1}{12} \times π \times 25 \times 8$

$∴$ Volume of water flows out = 100 × volume of spherical ball

$\Rightarrow \frac{1}{12} \times π \times 25 \times 8 = 100 \times \frac{4}{3} π R^{3}$

$\Rightarrow R^{3} = \frac{1}{8} \Rightarrow R = \frac{1}{2} c m = 0.5 c m$

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