Check my answer please?
Yuri is wrapping presents. The first box measures 9 inches by 12 inches by 2 inches. He has a second box with dimensions that are each half of the length of the first box.
How does the surface area of the second box compare with the surface are of the first box?
A. It is 1/2 the surface area of the first box.
B. It is 1/4 the surface area of the first box.
C. It is 1/8 the surface area of the first box.
D. It is 1/16 the surface area of the first box.
I put B.
correct.
To check your answer, let's calculate the surface area of both boxes and compare them.
The formula to find the surface area of a rectangular box is:
Surface Area = 2(lw + lh + wh)
For the first box, given its dimensions of 9 inches by 12 inches by 2 inches, plug in the values into the formula:
Surface Area = 2(9 * 12 + 9 * 2 + 12 * 2)
Surface Area = 2(108 + 18 + 24)
Surface Area = 2(150)
Surface Area = 300 square inches
Now let's calculate the dimensions of the second box. Each dimension is half the length of the first box, so:
Length of the second box = 9 / 2 = 4.5 inches
Width of the second box = 12 / 2 = 6 inches
Height of the second box = 2 / 2 = 1 inch
Plug these dimensions into the surface area formula for the second box:
Surface Area = 2(4.5 * 6 + 4.5 * 1 + 6 * 1)
Surface Area = 2(27 + 4.5 + 6)
Surface Area = 2(37.5)
Surface Area = 75 square inches
Now, let's compare the surface area of the second box to that of the first box:
75 square inches (surface area of the second box) / 300 square inches (surface area of the first box) = 1/4
Therefore, the correct answer is B. The surface area of the second box is 1/4 the surface area of the first box.