what percent of the pool is filled

Question

A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deep at the deep end (see figure). water is being pumped into the pool at 1/4 cubic meter per minute, and there is 1 meter of water at the deep end.

(a) what percent of the pool is filled?

(b) At what rate is the water level rising?

Answer 1

(a)

Step 1:

The length of the pool is .

The width of the pool is .

At the shallow end, depth is .

At the deep end, depth is .

Let us draw the front view pool.

In the front view of pool width of the pool is not shown.

The volume of the pool can be find out by sum of rectangle part and triangle prism part.

The color blue indicates that the amount of water filled in the pool.

Step 2:

Total volume of the pool is .

 

Total volume of the pool is

Step 3:

The volume of water already filled in pool is

The length of the water filled can be find out by applying the property of similar triangles.

From the property of similar triangle the ratio of any two sides are equal.

Therefore the length of the water filled is .

Substitute .

Step 4:

The percentage of water filled is

.

Solution :

Percentage of water filled is 12.5 %.