Answer:
You could not use a table with a top that is 2 1/2 feet long and 1 1/2 feet wide
Step-by-step explanation:
<u><em>The complete question is</em></u>
Elena needs to find a table that will fit three cube-shaped cases, each containing a frog.If the volume of each case is 1,000 cubic inches, could she use a table with a top that measures 2 1/2 feet long and 1 1/2 feet wide?Explain
step 1
Find the length side of the cube-shaped case
we know that
The volume of the cube is equal to
![V=b^3](https://tex.z-dn.net/?f=V%3Db%5E3)
where
b is the length side of the cube
we have
![V=1,000\ in^3](https://tex.z-dn.net/?f=V%3D1%2C000%5C%20in%5E3)
substitute
![1,000=b^3](https://tex.z-dn.net/?f=1%2C000%3Db%5E3)
solve for b
![b=10\ in](https://tex.z-dn.net/?f=b%3D10%5C%20in)
step 2
Convert feet to inches
![1\ ft=12\ in](https://tex.z-dn.net/?f=1%5C%20ft%3D12%5C%20in)
we have
![2\frac{1}{2}\ ft=2.5 (12)=30\ in](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B2%7D%5C%20ft%3D2.5%20%2812%29%3D30%5C%20in)
![1\frac{1}{2}\ ft=1.5 (12)=18\ in](https://tex.z-dn.net/?f=1%5Cfrac%7B1%7D%7B2%7D%5C%20ft%3D1.5%20%2812%29%3D18%5C%20in)
step 3
Compare the dimensions of the table with the dimensions of the cube-shaped case
30 > 10
The length of the table is greater than the length side of the cube
18> 10
The width of the table is greater than the length side of the cube
therefore
You could not use a table with a top that is 2 1/2 feet long and 1 1/2 feet wide