Question

Paul has three cube-shaped boxes. Each box is a different size

and they are stacked from the largest to the smallest. Some
information about the boxes is given below.
• The combined volume of the three boxes is 1,197 cubic inches.
• The area of one face of the medium box is 49 square inches. 7-9.7
. The volume of the smallest box is 218 cubic inches less than the volume of the
medium box.
1. What is the volume of the medium box? Explain.
The volume of the medium box is 343 Cubic inches
because since you know that the area of one roceis
49 you know that one side is 7.
2. What is the area of one face of the smallest box? Explain.
the area of one tace s 25 squarcin. because
you have to first find the area of the smallest box
which is 125 cubic in. Then you know that each side will
be 5 in you then mult. Sok to get the area of one tock
which is naarein.
3. What is the edge length of the largest box? Explain.
The edge length of the loroest boxis a because the
a volume of the large box is 729 Cubic inches.
4. What is the total height of the stack of boxes? How do you know?
The total height is 21 inches because you add are
of the measurements of each side from each box and
you get 21.
5. Paul wants to gift wrap the boxes. He has 1,000 in. of wrapping
paper. Does Paul have enough paper to wrap all three boxes?
Explain
5. IS THE ONE I NEED HELP WITH

Answer 1

See explanation

Explanation:

Paul has three cube-shaped boxes. Each box is a different size and they are stacked from the largest to the smallest. Some information about the boxes is given below.

• The combined volume of the three boxes is 1,197 cubic inches.
• The area of one face of the medium box is 49 square inches.
• The volume of the smallest box is 218 cubic inches less than the volume of the medium box.

1. The medium box has the area of one face of 49 square inches, then

`a^2=49\\ \\a=7\ inches`

is the side length.

The volume of the medium box is

`a^3=7^3=343\ in^3.`

2. The volume of the smallest box is 218 cubic inches less than the volume of the medium box, then the volume of the smallest box is

`343-218=125\ in^3.`

Ib is the side length, then

`b^3=125\\ \\b=5\ inches`

The area of one face is

`b^2=5^2=25\ in^2.`

3. The volume of the largest box is

`1,197-343-125=729\ in^3,`

then if c is the side length,

`c^3=729\\ \\c=9\ inches.`

4. The total height of the stack is the sum of all sides lengths:

`a+b+c=7+5+9=21\ inches`

5. Find the surface area of each box:

• small
  `6b^2=6\cdot 5^2=6\cdot 25=150\ in^2;`
• medium
  `6a^2=6\cdot 7^2=6\cdot 49=294\ in^2;`
• large
  `6c^2=6\cdot 9^2=6\cdot 81=486\ in^2.`

In total, Paul needs

`150+294+486=930\ in^2`

of wrapping paper. He has 1,000 square inches, so Paul has enough paper to wrap all 3 boxes.