The question is down there

Question

A large rectangular swimming pool is 1,000 feet long, 100 feet wide, and 10 feet deep. The pool is filled to the top with water.

1. What is the area of the surface of the water in the pool?
2. How much water does the pool hold?
3. Express your answers to the previous two questions as powers of 10.

Answer 1

Hi Cam,

This is a pretty simple surface area / volume problem, once you break the problem into its component parts. The problem gives us the dimensions of the swimming pool, which is rectangular — in three dimensions, we can visualize the pool as a rectangular prism (or cuboid), with a length of 1000 ft, a width of 100 ft, and a height or depth of 10 ft.

The first part of the problem asks for the area of the surface of the water in the pool. Assuming the pool is perfectly filled, the dimensions of the water are exactly those of the pool itself. The surface of the water then accounts for one side of the pool, the top, which is a function of the length and width, or l x w (the equation for the area of any rectangle). This means we multiply 1,000 ft by 100 ft, and get 100,000 square ft, or 10^4 ft^2.

The second part of the problem asks for how much water the pool holds which, assuming the pool is perfectly filled with water, is the same as the volume of the pool. We find volume by multiplying the length by the width by the height, or l x w x h. This means we multiply 1,000 ft by 100 ft by 10 ft, which gives us an answer of 1,000,000 cubic feet, or 10^5 ft^3.

Hope this helps!