Water is flowing at the rate of 15km/hour through a pipe of diameter 14 cm into a cuboidal pond which - Maths - Surface Areas and Volumes

Question

Water is flowing at the rate of 15km/hour through a pipe of
diameter 14 cm into a cuboidal pond which is 50 m long and 44 m
wide In what time the level of water in the pond rise by 21
cm?

Lalit Mehra · Accepted Answer

Let the level of water in the pond rises by 21 cm in t hours.

Speed of water = 15 km/hr

$Diameter of pipe = 14 cm = \frac{14}{100} m ∴ Radius of the pipe, r = \frac{7}{100} m$

Volume of water flowing out of the pipe in 1 hour

= π r²h

$= \frac{22}{7} \times (\frac{7}{100} m)^{2} \times 15000 m$

= 231 m³

∴ Volume of water flowing out of the pipe in t hours = 231 t m³.

Volume of water in the cuboidal pond

$= 50 m \times 4 4 m \times \frac{21}{100} m (∵ Volume of cuboid = l b h)$

= 462 m³

Volume of water flowing out of the pipe in t hours = Volume of water in the cuboidal pond

∴ 231 t = 462

$\Rightarrow t = \frac{462}{231} = 2$

Thus, the water in the pond rise by 21 cm in 2 hours.

50

Water is flowing at the rate of 15km/hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time the level of water in the pond rise by 21 cm?