A swimming pool measures 25 m long and 10 m wide. It has a shallow end that is 1 m deep and gradually slopes down to a depth of 4 m at the deep end. The inside walls of the pool need repainting. Calculate the total area of the surfaces to be painted, to the nearest square metre
the long sides are trapezoids with area (1+4)/2 * 25
The ends are rectangles, with areas 1*10 and 4*10
the bottom is a rectangle with area 10*√(3^2 + 25^2)
To calculate the total area of the surfaces to be painted, we need to find the area of the floor, the walls, and the surface of the water.
1. Area of the floor:
The floor of the pool is a rectangle with dimensions 25 m by 10 m. Therefore, the area of the floor is:
Area of the floor = Length x Width = 25 m x 10 m = 250 square meters.
2. Area of the walls:
The walls of the pool consist of two long walls and two short walls. Let's calculate the area of each wall separately.
Long walls:
The long walls are the sides with a length of 25 m. Since the depth changes from 1 m to 4 m, we will calculate the average depth.
Average depth of the long walls = (1 m + 4 m) / 2 = 2.5 m
The area of each long wall is equal to the product of the average depth and the length of the wall:
Area of each long wall = Length x Average Depth = 25 m x 2.5 m = 62.5 square meters
Since there are two long walls, the total area of the long walls is:
Total area of long walls = 2 x 62.5 square meters = 125 square meters
Short walls:
The short walls are the sides with a length of 10 m. Since the depth is constant at 1 m, the area of each short wall is:
Area of each short wall = Length x Depth = 10 m x 1 m = 10 square meters
Since there are two short walls, the total area of the short walls is:
Total area of short walls = 2 x 10 square meters = 20 square meters
Total area of the walls = Total area of long walls + Total area of short walls
Total area of the walls = 125 square meters + 20 square meters = 145 square meters
3. Surface area of the water:
The surface area of the water is equal to the area of the floor, as the water fills the entire pool.
Therefore, the total area of the surfaces to be painted is equal to the area of the floor plus the area of the walls:
Total area to be painted = Area of the floor + Total area of the walls
Total area to be painted = 250 square meters + 145 square meters = 395 square meters
So, the total area of the surfaces to be painted is approximately 395 square meters.
To calculate the total area of the surfaces to be painted, we need to consider the walls and the bottom of the pool separately.
1. Calculate the area of the walls:
Since the shallow end of the pool is 1 m deep, all the vertical walls have the same height of 1 m. The shallow end and the deep end of the pool have different widths, so we need to calculate the area for each separately.
- Calculate the area of the shallow end walls:
The height is 1 m, and the width is 10 m (the width of the pool). So, the area of the shallow end walls is 1 m x 10 m = 10 square meters.
- Calculate the area of the deep end walls:
The height is 4 m (the maximum depth of the pool), and the width is also 10 m. So, the area of the deep end walls is 4 m x 10 m = 40 square meters.
Add the areas of the shallow end walls and the deep end walls to get the total area of the wall surfaces: 10 square meters + 40 square meters = 50 square meters.
2. Calculate the area of the bottom:
The bottom of the pool is a rectangle with a length of 25 m and a width of 10 m. So, the area of the bottom is 25 m x 10 m = 250 square meters.
Now, add the area of the walls (50 square meters) to the area of the bottom (250 square meters) to find the total area of the surfaces to be painted: 50 square meters + 250 square meters = 300 square meters.
Therefore, the total area of the surfaces to be painted is 300 square meters (rounded to the nearest square meter).