Question 34 (Choice 1) - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Aug. 4, 2023 by Teachoo

Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm? What should be the speed of water if the rise in water level is to be attained in 1 hour

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Let length of pipe for filling whole pond be h m.
So, Volume of pipe = Volume of cuboidal pond
Volume of pipe
Pipe is in form of cylinder where
Let Height = h m
Diameter = 14 cm
So, Radius = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 = 14/2 = 7 cm
= 𝟕/𝟏𝟎𝟎 m
Volume of pipe = Volume of cylinder
= 𝜋r2h
= 𝝅(𝟕/𝟏𝟎𝟎)^𝟐 h
= 22/7 × 7/100 × 7/100 × h = (𝟐𝟐 × 𝟕)/𝟏𝟎𝟎𝟎𝟎 h
Volume of cuboidal pond
Pond is in form cuboid where
Length = l = 50 m
Breadth = b = 44 m
Height = h = 21 cm = 𝟐𝟏/𝟏𝟎𝟎 m
Volume of pond = lbh
= 50 × 44 × 𝟐𝟏/𝟏𝟎𝟎
= (44\ × 21)/2
= 22 × 21
Now,
Volume of pipe = Volume of pond
(𝟐𝟐 × 𝟕)/𝟏𝟎𝟎𝟎𝟎h = 22 × 21
h = (22 × 21 × 10000)/(22 × 7)
h = 30,000 m
h = 30 km
Now,
Water in pipe flows at rate 15 km/hr
So,
15 km travels in pipe in = 1 hour
1 km travels in pipe in = 1/15 hour
30 km travels in pipe in = 30/15 hour
= 2 hours
So, in 2 hours, the pond will be filled
We also need to find the speed of water if the rise in water level is to be attained in 1 hour.
We know that
Pond takes 2 hours to attain rise at given speed = 15 km/h
If it wants to fill in 1 hour, it’s speed should be double
Therefore,
Speed of water required to attain rise in 1 hour = 15 × 2
= 30 km/h

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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