
Jordan K. answered 09/03/15
Tutor
4.9
(79)
Nationally Certified Math Teacher (grades 6 through 12)
Hi Jennifer,
Let's begin by using a letter to represent our unknown:
h = height (when tank "filled to the brim")
Now let's write an equation in words to express what is said in the problem:
Full Volume = Current Volume plus
Added Volume
Added Volume
Now let's recall the Volume formula for a rectangular solid:
Volume = Length x Width x Height
Now let's plug in our known values into our Full Volume word equation to calculate the Full Volume:
Full Volume = Current Volume + Added Volume
Full Volume = (46 x 24 x 14) + 4,416
Full Volume = 15,456 + 4,416
Full Volume = 19,872 cm3
Now that we know the Full Volume of the tank, we can calculate it's height when "filled to the brim" using the Volume formula for a rectangular solid:
Volume = Length x Width x Height
19,872 = 46 x 24 x h
1,104h = 19,872
h = 19,872 / 1,104
h = 18 cm
(height when tank "filled to the brim")
(height when tank "filled to the brim")
We needed a two step approach to this problem:
1. Calculate the Full Volume of the tank based upon the Current Volume plus the Added Volume.
2. Calculate the height of the tank "when filled to the brim" when knowing the Full Volume of the tank.
Thanks for submitting this intriguing problem !!
Glad to be of help.
God bless, Jordan.