Question

1. List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.) length = 8in. width=5in. Height=1in.
2. Describe the shape of the cross section when the box is cut parallel to the base.
3. What is the surface area of the box?
4. What is the surface area of the box if it is scaled up by a factor of 10?
5. What is the volume of the box? 40in.
6. What is the volume of the box if it is scaled down by a factor of 1/10?

Answer 1

i need help with #2, 3, 4 and 6

Answer 2

Well, #2 asks for a description of the cross section. We know that cross section is just cutting something in half. And the next sentence says we're cutting it parallel to the base, or to the ground, meaning it's being cut in half horizontally.

Answer 3

Since it's being cut in half horizontally, the height is going to be the only thing decreasing. If it was being cut vertically, then width or length would be reduced.

Since we know that the height is being cut in half, we can describe the dimensions of the cross section as:

L = 8in
W = 5in
H = 0.5in

Answer 4

For #3, I'm gonna give you the formula. The formula for SA is:

\[SA = 2(lw + lh + wh)\]

The formula is self explanatory, just plug in the numbers and you'll have your surface area

Answer 5

For #4, we're introducing scale factor. What is scale factor? Well the meaning lies within the name, it's just scaling your factors. When scaling by 10, it just means that every line and side is increasing by a factor of 10.

So for each side, you would multiply by 10. And then find the surface area.

Or alternatively, you can just multiply the surface area you got in #3, by 10 and get the same answer.

Answer 6

Now #6 is the same concept as what we did in #4, however instead of multiplying, we divide by 10 to get our answer.