## Water is flowing through a cylindrical pipe of internal diameter 2cm, into a cylindrical tank of base radius 40 cm at the rate of 0.7m/sec. By how much will the water rise in the tank in half an hour?     1. Class 10
2. Solutions of Sample Papers for Class 10 Boards
3. CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Transcript

Let Rise in water level be h meters Now, Volume of water through pipe in 30 minutes= Volume of tank Volume of water through pipe in 30 minutes Pipe is in form of cylinder where Diameter = 2 cm So, Radius = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 = 2/2 = 1 cm = 𝟏/𝟏𝟎𝟎 m Now, Rate of filling water is 0.7 m/sec So, In 1 second, water flowing through pipe = 0.7 m Water flowing through pipe in in 30 minutes = 0.7 × 30 × 60 = 1260 m Thus, Height of cylindrical pipe = 1260 m Now, Volume of water through pipe = Volume of cylinder = 𝜋r2h = 𝜋(1/100)^2 × 1260 = 𝜋 × 1/100 × 1/100 × 1260 = (𝝅 × 𝟏𝟐𝟔)/𝟏𝟎𝟎𝟎 m3 Volume of tank Tank is in form cylinder where Radius = r = 40 cm = 40/100 m = 𝟒/𝟏𝟎 m Let rise in water level = h m Volume of tank = 𝜋r2h = 𝜋 × (4/10)^2 × h = 𝟏𝟔𝝅𝒉/𝟏𝟎𝟎 m3 Now, Volume of pipe = Volume of tank (𝝅 × 𝟏𝟐𝟔)/𝟏𝟎𝟎𝟎 = 𝟏𝟔𝝅𝒉/𝟏𝟎𝟎 (𝜋 × 126)/1000 ×100/(16𝜋 ) = h 126/160 = h ℎ = 126/160 m ℎ = 126/160 × 100 cm ℎ = 1260/16 cm h = 78.75 cm

CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Class 10
Solutions of Sample Papers for Class 10 Boards 