3. A box company produces two sizes of pizza boxes. The smaller box has a surface area of 260 square inches. The larger box has a length, width, and height that are twice those of the smaller box. What is the surface area of the larger box?
A. 520 square inches
B. 1,040 square inches
C. 1,560 square inches
D. It cannot be determined from the information given.
Is the answer D ??? Don't I need more information to solve this problem??
As=2(W*H) + 2(L*H) + 2(W*L=Surface area.
Doubling each dimension multiplies each
term by 4 which multiplies our Eq by 4.
Therefore, the surface area of the larger box is 4 times the smaller box.
As = 4 * 260 = 1,040in^2 = "B"
To solve this problem, we can use the fact that the larger box has dimensions twice as big as the smaller box. Let's start by finding the dimensions of the smaller box.
Let's assume the length of the smaller box is L inches, the width is W inches, and the height is H inches. The surface area of a rectangular box can be found using the formula:
Surface Area = 2(LW + LH + WH)
Given that the surface area of the smaller box is 260 square inches, we have:
2(LW + LH + WH) = 260
Now, let's look at the larger box. According to the problem statement, all three dimensions of the larger box are twice as big as the smaller box. Therefore, the length of the larger box is 2L inches, the width is 2W inches, and the height is 2H inches.
The surface area of the larger box can be found using the same formula:
Surface Area = 2(2L * 2W + 2L * 2H + 2W * 2H)
Surface Area = 2 * 4(LW + LH + WH)
Surface Area = 8(LW + LH + WH)
Substituting the value 260 for the surface area of the smaller box, we have:
Surface Area = 8 * 260
Surface Area = 2080 square inches
Therefore, the surface area of the larger box is 2080 square inches.
Checking the given answer choices:
A. 520 square inches - This is incorrect since we found the surface area to be 2080 square inches, which is much larger than 520 square inches.
B. 1,040 square inches - This is incorrect since we found the surface area to be 2080 square inches, which is much larger than 1040 square inches.
C. 1,560 square inches - This is incorrect since we found the surface area to be 2080 square inches, which is much larger than 1560 square inches.
D. It cannot be determined from the information given. - This is incorrect since we were able to determine the surface area of the larger box using the given information.
Hence, none of the answer choices are correct. The correct answer is not listed among the given options.