Question

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

Answer 1

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here is your answer

Answer 2

Answer:

100

Step-by-step explanation:

Let x be the number of lead shots dropped in the vessel.

Height of vessel = 8 cm.

Radius of vessel(R) = 5 cm.

Radius of lead shots(r) = 0.5 cm.

∴ (1/4) * Volume of cone = x * Volume of lead shots

⇒ (1/4) * (1/3) πR²h = x * (4/3) πr³

⇒ (1/12) πR²h = x * (4/3)πr³

⇒ (1/4)πR²h = x * 4πr³

⇒ R²h = 16xr³

⇒ 5² * 8 = 16 * x * 0.5³

⇒ 200 = x * 2

⇒ x = 100.

Therefore, number of lead shots dropped in the vessel = 100.

Hope it helps!