**Solving volume equations worksheet :**

Worksheet on solving volume equations is much useful to the students who would like to practice solving word problems on volume of rectangular prisms.

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 ?

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.

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.

**Problem 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.

**Problem 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.

**Problem 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.

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