Question

mrs. defilippis is moving!
there is so much to do and i cannot possibly figure it all out alone!
please help me!
my family needs a moving truck that has a volume of
1,200 cubic feet. our moving company said to rent the
medium - mover. the dimensions are 17.25 feet long,
7.2 feet wide and 9.5 feet tall. will this be large enough
to hold all of my family’s belongings? show how you
know!
the moving company that we are using, mighty movers, rents out 3
different truck sizes. the mini - mover is 9.5 feet long, 6.5 feet wide and 6.5
feet tall. the medium - mover is 17.25 feet long, 7.2 feet wide and 9.5 feet tall.
the mega - mover is 24.25 feet long, 8.5 feet wide and 10.25 feet tall. please
help me calculate the volume of all three trucks rounded to the nearest tenth.
mini - mover:
______ cubic feet
medium - mover:
______ cubic feet
mega - mover:
______ cubic feet

Explanation:

Step1: Calculate Mini - Mover Volume

The formula for the volume of a rectangular prism (which a truck can be considered as) is \(V = l\times w\times h\). For the Mini - Mover, \(l = 9.5\) feet, \(w = 6.5\) feet, and \(h = 6.5\) feet.
So, \(V=9.5\times6.5\times6.5\)
First, calculate \(6.5\times6.5 = 42.25\)
Then, \(9.5\times42.25=401.375\approx401.4\) (rounded to the nearest tenth)

Step2: Calculate Medium - Mover Volume

For the Medium - Mover, \(l = 17.25\) feet, \(w = 7.2\) feet, and \(h = 9.5\) feet.
Using the volume formula \(V=l\times w\times h\)
\(V = 17.25\times7.2\times9.5\)
First, \(17.25\times7.2 = 124.2\)
Then, \(124.2\times9.5 = 1179.9\)

Step3: Calculate Mega - Mover Volume

For the Mega - Mover, \(l = 24.25\) feet, \(w = 8.5\) feet, and \(h = 10.25\) feet.
Using the volume formula \(V=l\times w\times h\)
\(V=24.25\times8.5\times10.25\)
First, \(24.25\times8.5 = 206.125\)
Then, \(206.125\times10.25=206.125\times(10 + 0.25)=206.125\times10+206.125\times0.25=2061.25 + 51.53125 = 2112.78125\approx2112.8\) (rounded to the nearest tenth)

Answer:

Mini - Mover: \(401.4\) cubic feet
Medium - Mover: \(1179.9\) cubic feet
Mega - Mover: \(2112.8\) cubic feet