A circular pond in a city garden has a 30 meter fence around it and it is 2 meters deep. Calculate the volume of the water it can hold.
To calculate the volume of water that the circular pond can hold, we need to find its area and multiply it by its height.
First, let's calculate the radius of the circular pond using the fence around it. The fence is 30 meters long, which is the circumference of the pond. We can use the formula for the circumference of a circle:
C = 2πr,
where C is the circumference and r is the radius.
30 = 2πr,
Dividing both sides by 2π, we find:
r = 30 / (2π) ≈ 4.77 meters.
Next, let's calculate the area of the circular pond using the formula for the area of a circle:
A = πr²,
where A is the area and r is the radius.
A = π(4.77)² ≈ 71.5 square meters.
Finally, we can calculate the volume of the water in the pond by multiplying the area by the height:
V = A × h,
where V is the volume, A is the area, and h is the height.
V = 71.5 × 2 = 143 cubic meters.
Therefore, the circular pond can hold approximately 143 cubic meters of water.
To calculate the volume of water the circular pond can hold, we need to determine the area of the circular base and then multiply it by the depth of the pond.
1. Determine the radius of the circular pond:
The perimeter of the fence around the pond is equal to the circumference of the circle.
Circumference = 2 * π * radius
30 meters = 2 * π * radius
radius = 30 meters / (2 * π)
radius ≈ 4.77 meters (rounded to two decimal places)
2. Calculate the area of the circular base:
Area = π * radius^2
Area = π * (4.77 meters)^2
Area ≈ 71.68 square meters (rounded to two decimal places)
3. Calculate the volume of the water:
Volume = Area * Depth
Volume = 71.68 square meters * 2 meters
Volume ≈ 143.36 cubic meters (rounded to two decimal places)
Therefore, the circular pond can hold approximately 143.36 cubic meters of water.