CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard
Last updated at Dec. 13, 2024 by Teachoo
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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 = π·πππππ‘ππ/2 = 14/2 = 7 cm = π/πππ m Volume of pipe = Volume of cylinder = πr2h = π (π/πππ)^π h = 22/7 Γ 7/100 Γ 7/100 Γ h = (ππ Γ π)/πππππ h Volume of cuboidal pond Pond is in form cuboid where Length = l = 50 m Breadth = b = 44 m Height = h = 21 cm = ππ/πππ m Volume of pond = lbh = 50 Γ 44 Γ ππ/πππ = (44\ Γ 21)/2 = 22 Γ 21 Now, Volume of pipe = Volume of pond (ππ Γ π)/πππππh = 22 Γ 21 h = (22 Γ 21 Γ 10000)/(22 Γ 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, itβs speed should be double Therefore, Speed of water required to attain rise in 1 hour = 15 Γ 2 = 30 km/h
