Answer :
The total volume of concrete required to line the pond is approximately 0.973 cubic meters.
We need to consider both the inner volume of the pond and the outer volume when concrete is added. Let's start with the given dimensions:
- Radius of the pond, r = 1.5 meters
- Depth of the pond, h = 1 meter
- Thickness of the concrete lining, t = 0.1 meters
Calculate the volume of the pond without concrete lining
The volume of a cylindrical shape (which the pond resembles) is given by the formula:
[tex]V = \pi r^2 h[/tex]
Here,
[tex]r = 1.5 \text{ m}[/tex]
[tex]h = 1 \text{ m}[/tex]
So,
[tex]V_{inner} = \pi (1.5)^2 (1) = \pi (2.25) = 2.25\pi \text{ cubic meters}[/tex]
Calculate the volume of the pond with an additional concrete lining
For the outer volume of the pond (including the concrete), the new radius will be:
[tex]r_{outer} = r + t = 1.5 + 0.1 = 1.6 \text{ meters}[/tex]
So,
[tex]V_{outer} = \pi (1.6)^2 (1) = \pi (2.56) = 2.56\pi \text{ cubic meters}[/tex]
Find the volume of the concrete required
The concrete will occupy the difference between the outer volume and the inner volume:
[tex]V_{concrete} = V_{outer} - V_{inner}[/tex]
[tex]V_{concrete} = 2.56\pi - 2.25\pi[/tex]
[tex]V_{concrete} = (2.56 - 2.25)\pi[/tex]
[tex]V_{concrete} = 0.31\pi[/tex]
Using an approximate value for [tex]\pi[/tex] (about 3.14159):
[tex]V_{concrete} \approx 0.31 \times 3.14159 \approx 0.973 \text{ cubic meters}[/tex]
