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?
Choices are:
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??
The surface area of two similar figures or solids is proportional to the square of the ratio of linear dimensions.
From
"The larger box has a length, width, and height that are twice those of the smaller box"
we conclude that the ratio of linear dimensions is 2.
2²=4.
What is 4*260?
No, the answer is not D. You have enough information to solve the problem. Let me explain how to find the surface area of the larger box.
Given that the surface area of the smaller box is 260 square inches, we can label its dimensions as length (L), width (W), and height (H). Since the larger box has dimensions twice those of the smaller box, the dimensions of the larger box would be 2L, 2W, and 2H.
The surface area of a rectangular box is determined by the formula:
Surface Area = 2(LW + LH + WH).
For the smaller box, this becomes:
260 = 2(LW + LH + WH).
Now, we can substitute the larger box's dimensions into the formula:
Surface Area of the larger box = 2(2L)(2W) + 2(2L)(2H) + 2(2W)(2H) = 16(LW + LH + WH).
Since the surface area of the larger box is 16 times that of the smaller box, we can find the surface area of the larger box by multiplying 260 by 16:
Surface Area of the larger box = 260 * 16 = 4160 square inches.
Therefore, the correct answer is not D, but rather the surface area of the larger box is 4160 square inches. However, since none of the given choices match this value, it seems like there might have been a mistake in the problem or the answer choices.