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. it the pools are filled all the way to the top, what is the volume of each pool?

Answer 1

Answer:

The volumes of four rectangular prism are 16,54,128,250 cubic feet.

Step-by-step explanation:

Given : 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.

To find : What is the volume of each pool?

Solution :

Let x be the height of the pool,

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

According to question,

The length of each pool is twice the width and twice the depth.

So, width = x , length = 2x and height = x

The equation form to find volume is $V=l\times w\times h$

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

Now,

At x=2

$V=2(2)^3$

$V=2(8)$

$V=16\text{ ft.}^3$

At x=3

$V=2(3)^3$

$V=2(27)$

$V=54\text{ ft.}^3$

At x=4

$V=2(4)^3$

$V=2(64)$

$V=128\text{ ft.}^3$

At x=5

$V=2(5)^3$

$V=2(125)$

$V=250\text{ ft.}^3$

Therefore, The volumes of four rectangular prism are 16,54,128,250 cubic feet.

Answer 2

The equation to find out the volume in this case is V=x*x*2x, or V=2x^3. Use this we can get that the volumes would be 16, 54, 128, and 250.