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In the rainy season, I forget a cylindrical bottle on the roof. The base radius of the bottle is 10 cm and the height is 50 cm. When the rain comes raindrops are falling inside the bottle. A raindrop is in the form of a sphere of radius 10 mm. If the rate of raindrops per min is 350 drops / square meter. How much time bottle will be filled with Raindrops?

In the rainy season, I forget a cylindrical bottle on the roof. The base radius of the bottle is 10 cm and the height is 50 cm. When the rain comes raindrops are falling inside the bottle. A raindrop is in the form of a sphere of radius 10 mm. If the rate of raindrops per min is 350 drops / square meter. How much time bottle will be filled with Raindrops? Correct Answer 125 / 22 hr

Given:

The base radius of the bottle = 10 cm

height of the bottle = 50 cm

Radius of sphere = 10 mm

the rate of fall of raindrops = 350 drops / square metre / min

Formula use:

Area of circle = πr2

Volume of sphere = 4 / 3πr3

Number of drops needed to fill the bottle = volume of bottle / volume of rain drop

Calculations:

Base area of the bottle =  2200/7 × 350/10,000 = 11 cm2

Number of drops falling in the bottle / min. = 2200/7 × 350/10,000 = 11 drops.

Number of drops needed to fill the bottle,

⇒ (22/7 × 10 × 10 × 50)/(4/3 × 22/7 × 103)

⇒ 3750 drops

Time to fill the bottle = 3750/11 min

(In hour) = 3750/(11 × 60) = 125/22 hr.

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