# SOLVING VOLUME EQUATIONS

## About "Solving volume equations"

Solving volume equations :

We can use the formula for the volume of a rectangular prism to write an equation. Then solve the equation to find missing measurements for a prism.

## Solving volume equations - Examples

Example 1 :

Samuel has an ant farm with a volume of 375 cubic inches. The width of the ant farm is 2.5 inches and the length is 15 inches. What is the height of Samuel’s ant farm?

Solution :

From the given information, it is clear that the shape of ant form is rectangular prism.

Let us write formula for volume of rectangular prism (ant form)

V  =  l x w x h

Use the formula to write an equation.

Plug V  =  375, w  =  2.5 and l  =  15

375  =  15 x 2.5 x h

375  =  37.5 x h

Divide both sides of the equation by 37.5

375/37.5  =  (37.5 x h)/37.5

10  =  h

Hence, the height of the form is 10 inches.

Example 2 :

A terrarium is shaped like a rectangular prism with a volume of 5200 cubic inches. The prism is 13 inches wide and 16 inches deep. Find the length of the terrarium.

Solution :

From the given information, we can have the following figure.

Let us write formula for volume of rectangular prism.

V  =  l x w x h

Use the formula to write an equation.

Plug V  =  5200, w  =  13 and h  =  16

5200  =  l x 13 x 16

5200  =  l x 208

Divide both sides of the equation by 208

5200/208  =  (l x 208)/208

25  =  l

Hence, the length of terrarium is 25 inches.

Example 3 :

A rectangular swimming pool is in shape of rectangular prism with a volume of 393 3/4 cubic meters. The swimming pool is 15 meters long and 2 1/2 meters deep. Find the width of the pool.

Solution :

From the given information, we can have the following figure.

Let us write formula for volume of rectangular prism.

V  =  l x w x h

Use the formula to write an equation.

Plug V  =  393 3/4, l  =  15 and h  =  2 1/2

393 3/4  =  15 x w x 2 1/2

1575/4  =  15 x w x 5/2

1575/4  =  w x 75/2

Multiply both sides of the equation by 2/75

(1575/4) x (2/75)  =  (w x 75/2) x 2/75

21/2  =  w

10 1/2  =  w

Hence, the width of the swimming pool is 10 1/2 meters.

After having gone through the stuff given above, we hope that the students would have understood "How to solve volume equations".

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