Question

A swimming pool is 50 metres long and 15 metres wide. Its shallow and deeep ends are 1.5 metres and 4.5 metres deep, respectively. If its bottom of the pool slopes uniformly, find the amount of water required to fill the pool.

Answer 1

1 m shallow at one end and 8 m deep at other end. They are parallel sides. 
(1/2 * (8+1)* 50)*25 
4.5 *1250
5625 m^3 is the volume 
You calculate the area of the trapezium and multiply by the width of the pool to get the volume. 
length side area = 2 sides=> they are trapeziums 
parallel sides are 1m & 8m perpendicular distance = 50 
1/2 * (8+1)* 50=225 m^2
225*2 = 450 m^2
II side 25*1= 25m^2
III side25*8= 200m^2 
bottom surface 
The distance along the length of pool from 1m depth to 8m depth, length can be calculated by pythagoras theorem. This length is sqrt(50^2+7^2)=50.5 m
width = 25 m 
Area of base = 50.5 *25= 1262 m^2 
Total area = 450+25+200+1262 m^2
=1937m^2

Answer 2

Question:-

A swimming pool is 50 meters long and 15 meters wide. It's shallow and deep ends are 1.5 meters and 4.5 meters deep respectively. Find the amount of water required to fill the pool.

Required Answer:-

Given:-

• Length of the swimming pool = 50 meters
• Width of the swimming pool = 15 meters.
• Height of the shallow end of the pool = 1.5 meters
• Height of the deep end of the pool = 4.5 meters.

To find:-

• The amount of water required to fill the pool

Solution:-

To find the amount of the water required to fill the pool, first we have to find the volume of the pool. And to find the volume of the pool we have to find the area of the pool which is in trapezium shape.

We know that,

• Area of trapezium = ½(Sum of the parallel sides)(Perpendicular difference between them)

From the figure of the pool, we get:-

• Parallel sides of the pool are at a length of 1.5m and 4.5 m
• Distance between the parallel sides is 50m

Substituting the values:-

Area of the pool = ½(1.5 + 4.5)(50)

=> Area of the pool = 1/2 × 6 × 50

=> Area of the pool = 150m^(2)

Again,

Volume of the pool = Area of the pool × width of the pool

=> Volume of the pool = 150 × 15

=> Volume of the pool = 2250m^(3)

Now,

We know that:-

• 1m^(3) = 1 kilolitre

∴ 2250m^(30) = 2250 kiloliters

Hence, the amount of water required to fill the pool is 2250 kilolitres