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? 

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?

The time taken by the pipe to fill the pond with water up to 21 cm is 2 hours.

1. Calculate the Volume of Water Flowing In:

   • Given the diameter of the pipe (14 cm), we can find its radius:
     • Radius = Diameter / 2 = 14 cm / 2 = 7 cm = 0.07 m
   • The rate of flow is 15 km/h, which is 15000 m/h in SI units.
   • Using the formula for the volume of a cylinder (V = πr²h):
     • Volume of water flowing through the pipe in one hour = π × (0.07)² × 15000 m³

2. Calculate the Volume of the Cuboidal Pond:

   • Given the dimensions of the cuboidal pond (length, width, and depth), we can calculate its volume:
     • Volume of pond = Length × Width × Depth
3. Find the Time Taken to Fill the Pond:
   Divide the volume of the pond by the volume of water flowing through the pipe in one hour:
   Time taken = Volume of pond / Volume of water flowing through the pipe in one hour.

Calculate the Volume of Water Flowing In:

Volume of water flowing through the pipe in one hour = π × (0.07)^2 × 15000 m^3

Volume ≈ (22/7) × 0.0049 × 15000 m^3

Volume ≈ 231 m^3

Calculate the Volume of the Cuboidal Pond:

Volume of pond = Length × Width × Depth

Volume = 50 × 44 × 0.21 m^3

Volume = 462 m^3

Find the Time Taken to Fill the Pond:

Time taken = Volume of pond / Volume of water flowing through the pipe in one hour

Time taken = 462 m^3 / 231 m^3

Time taken = 2 hours

Therefore, the time taken by the pipe to fill the pond with water up to 21 cm is 2 hours.

Volume of Cuboid and Volume of Cylinder

Cuboid:

A cuboid is a three-dimensional shape with six rectangular faces. The volume of a cuboid is the amount of space it occupies. The formula to calculate the volume of a cuboid is:

Volume of Cuboid = Length (l) × Breadth (b) × Height (h)

Cylinder:

A cylinder is a three-dimensional shape with two circular bases and a curved lateral surface. The volume of a cylinder is also the amount of space it occupies. The formula to calculate the volume of a cylinder is:

Volume of Cylinder = π × Radius² (r²) × Height (h)

Here are some key points to remember:

• π (pi) is a mathematical constant with an approximate value of 3.14159.
• l, b, and h for the cuboid and r and h for the cylinder represent the dimensions in the same unit (e.g., centimeters, meters).
• The volume is always expressed in cubic units (e.g., cm³, m³).

Example:

• A cuboid has a length of 5 cm, a breadth of 3 cm, and a height of 2 cm.

• Volume of Cuboid = 5 cm × 3 cm × 2 cm = 30 cm³

• A cylinder has a radius of 4 cm and a height of 6 cm.

• Volume of Cylinder = π × 4² cm × 6 cm ≈ 75.39 cm³

Remember:

• A cube is a special type of cuboid where all the sides are equal. The volume of a cube can be calculated using the formula: Volume of Cube = Side³.
• There are other formulas for calculating the surface area of both cuboids and cylinders.