**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.

**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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