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Q.

A vessel is in the form of an inverted cone. Its height is 8 cm and radius of its top is 5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, $\frac{1}{4}$ of the water flows out. Then the number of lead shots dropped into the water is

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a

100

b

90

c

80

d

70

answer is A.

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Detailed Solution

Height of inverted cone

= 8 cm

Radius of inverted cone $= 5 cm$

Radius of sphere $= 0.5 cm$

$n (volume of sphere) = \frac{1}{4} (volume of cone)$

$n [\frac{4}{3} π {(\frac{1}{2})}^{3}] = \frac{1}{4} [\frac{1}{3} π {(5)}^{2} \times 8]$

$n = 100$

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A vessel is in the form of an inverted cone. Its height is 8 cm and radius of its top is 5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, 14 of the water flows out. Then the number of lead shots dropped into the water is