Question

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

Answer 1

To find the time it takes for the water level to rise by 21 cm, we need to calculate the volume of water that flows into the pond. The time is approximately 1.27 hours.

Step-by-step explanation:

To find the time it takes for the water level to rise by 21 cm, we need to calculate the volume of water that flows into the pond. The volume of water can be found by multiplying the cross-sectional area of the pipe (πr²) by the flow rate (velocity × area).

First, we convert the diameter of the pipe from cm to m by dividing it by 100. So, the radius of the pipe is 7/100 m.

The cross-sectional area of the pipe can be calculated as A = π(7/100)². Substituting the given values, we get A = 0.0154 m².

The flow rate of water can be calculated as Q = Velocity × Area. Substituting the given values, we get Q = 15 × 1000 × 0.0154 m³/hour.

To find the time it takes for the water level to rise by 21 cm, we divide the volume of water (Q) by the area of the pond (Length × Width).

Substituting the given values, we get the time = Q / (50 × 44 × 1) hours.

Simplifying the expression, we find that the time it takes for the water level to rise by 21 cm is approximately 1.27 hours.