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.
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