Question
A travel-size cereal box has dimensions of 3 in. x 1 in. x 4 in.
If it is redesigned to be a cube with the same surface area, what would be the length of each side in the cube?
*
2 points
2.3 inches
2.5 inches
3.5 inches
4 inches
If it is redesigned to be a cube with the same surface area, what would be the length of each side in the cube?
*
2 points
2.3 inches
2.5 inches
3.5 inches
4 inches
Answers
GPT 3.5
To find the surface area of the original cereal box, we need to calculate the area of each side and then add them all together.
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(3*1) + 2(3*4) + 2(1*4)
Surface Area = 2(3) + 2(12) + 2(4)
Surface Area = 6 + 24 + 8
Surface Area = 38 square inches
Since the redesigned cereal box will be a cube with the same surface area, we need to find the length of each side of the cube.
The formula for the surface area of a cube is 6s^2, where s is the length of each side.
So, 6s^2 = 38
s^2 = 38/6
s^2 = 6.33
s = sqrt(6.33)
s = 2.52
Therefore, the length of each side of the cube will be approximately 2.5 inches.
The correct answer is: 2.5 inches
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(3*1) + 2(3*4) + 2(1*4)
Surface Area = 2(3) + 2(12) + 2(4)
Surface Area = 6 + 24 + 8
Surface Area = 38 square inches
Since the redesigned cereal box will be a cube with the same surface area, we need to find the length of each side of the cube.
The formula for the surface area of a cube is 6s^2, where s is the length of each side.
So, 6s^2 = 38
s^2 = 38/6
s^2 = 6.33
s = sqrt(6.33)
s = 2.52
Therefore, the length of each side of the cube will be approximately 2.5 inches.
The correct answer is: 2.5 inches