Class 10 Maths Sample Paper 2019 | Q21 Choice 1

This 2019 CBSE class 10 Maths 3 mark question is from Surface Areas and Volumes. Concept tested: Computing volumes of rectangular cuboids and cylinders.

Question 21A: Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tank will rise by 21 cm.

Video Explanation

Explanatory Answer | Sample Paper 2019 Question 21 Choice 1

Step 1: Convert the units of all measurements to metres

Rate of flow of water through the pipe = 15 km/hr = 15000 m/hr
Diameter of pipe = 14 cm
Radius of the pipe, r = 7 cm = \\frac{7}{100}) m
Length of rectangular tank = 50 m
Width of rectangular tank = 44 m
Height to be filled in the tank = 21 cm = \\frac{21}{100}) m

Step 2: Compute the volume of water flowing through the pipe in 1 hour

Volume of water flowing in 1 hour = Rate of flow of water × Area of cross-section of pipe
= 15000 m/hr × (πr²) m²
= (15000 πr²) m³/hr
= 15000 × \\frac{22}{7}) × \\frac{7}{100}) × \\frac{7}{100}) m³/hr
= 231 m³

Step 3: Compute the volume of water filled when the level of water in the tank rises by 21 cm

Volume of water required in the rectangular tank = Length × Width × 21 cm
= 50 × 44 × \\frac{21}{100}) m³
= 22 × 21 m³
= 462 m³

Step 4: Compute the time taken by the water from pipe to fill 21 cm of the tank

Volume of water flowing in 1 hour = 231 m³/hr
Time taken by the pipe to fill 231 m³ = 1 hour
Volume of water required for a 21 cm rise in the level of the rectangular tank = 462 m³
Time taken for the level of water in the tank to increase by 21 cm = \\frac{462}{231}) = 2 hours