Question

One company makes inflatable swimming pools that come in four sizes of rectangular prisms. The length of each pool is twice the width and twice the depth . The depth of the pools are each a whole number from 2 to 5 feet. If the pools are filled all the way to the top, what is the volume?

Answer 1

Answer:

Given is :

One company makes inflatable swimming pools that come in four sizes of rectangular prisms.

The depth of the pools are each a whole number from 2 to 5 feet. This means 2,3,4 and 5.

Now, the length of each pool is twice the width and twice the depth .

The equation to find out the volume in this case is :

V=$x \times x\times 2x =2x^{3}$

So, when x = 2 feet, the length is 4 feet.

Volume is $2\times2\times4=16$ cubic feet

When x = 3 , the length is 6

Volume is $3\times3\times6=54$ cubic feet

When x = 4 , the length is 8

Volume is $4\times4\times8=128$ cubic feet

When x = 5 , the length is 10

Volume is $5\times5\times10=250$ cubic feet

Answer 2

If the pools are filled all the way to the top, its volume would be equal to 250 cubic feet.

How to calculate the volume of the pool?

Let the length of pool be L.

Let the width of pool be W.

Let the depth of pool be D.

Translating the word problem into an algebraic expression, we have;

L = 2W = 2D.

Also, the depth of the pools would range from 1 to 5.

Mathematically, the volume of this pool is given by this equation:

Volume = 2D × L × W.

When D = 2, we have:

Volume = 2(2) × 2 × 2

Volume = 16 cubic feet.

When D = 3, we have:

Volume = 2(3) × 3 × 3

Volume = 54 cubic feet.

When D = 4, we have:

Volume = 2(4) × 4 × 4

Volume = 128 cubic feet.

When D = 5, we have:

Volume = 2(5) × 5 × 5

Volume = 250 cubic feet.

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