Water was poured in a tank...

Question

Water was poured into a tank to a height of 14 cm. Another 4,416 cm to the third power of water with then poured into it until it reached its brim. What is the height of the tank? (L-46cm W-24cm H-14cm)

Answer 1

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

 

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")

 

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.