Question

A hemisphere of radius 21 cm is completely filled with milk. There is a hole in
the bottom whose radius is 0.1 cm. If rate of out flow of milk from the hole is
0.7 cm/sec, in how much time the hemisphere will be empty?
10 days 5 hours
10 days
9 days 7 hours
10 days 10 hours​

Answer 1

Given :- A hemisphere of radius 21 cm is completely filled with milk. There is a hole in the bottom whose radius is 0.1 cm. If rate of out flow of milk from the hole is 0.7 cm/sec, in how much time the hemisphere will be empty ?

A) 10 days 5 hours.

B) 10 days.

C) 9 days 7 hours.

D) 10 days 10 hours.

Solution :-

As we know :-

• Volume of hemisphere = (2/3) * π * (radius)³.
• water flows from hole is in the shape of a cylinder whose height is equal to rate of flow .
• Volume of cylinder = π * (radius)² * height.

given that,

→ Radius of hemisphere = 21cm.

So,

→ Volume of hemisphere = (2/3) * (22/7) * 21 * 21 * 21 = 2 * 22 * 441 = (44 * 441)cm³.

Now,

→ height of cylinder = 0.7 cm. (rate)

→ radius of cylinder = 0.1 cm.

So,

→ volume of cylinder = (22/7) * (0.1)² * 0.7) = 22 * (0.1)³ = 0.022 cm³.

we can say that,

→ in one second milk goes out from hole = 0.022 cm³.

Therefore,

→ The hemisphere will be empty in = (44 * 441) / (0.022) = (44 * 441 * 1000) / 22 = 882000 seconds.

Now,

→ 3600 seconds = 1 hour.

→ 1 second = (1/3600) hour.

→ 882000 seconds = (1/3600) * 882000 = 245 hours.

Now,

→ 24 hours = 1 day.

→ 1 hour = (1/24) day.

→ 245 hours. = (245/24) = (10 days + 5 hours.) (Option A) (Ans.)

Hence, the hemisphere will be empty in 10 days and 5 hours.

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