A travel-size cereal box has dimensions of 3 in. x 1.5 in. x 4.5 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) Responses 2.2 in 2.2 in 2.9 in 2.9 in 3.2 in 3.2 in 6.4 in
To find the surface area of the original cereal box, use the formula:
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(3)(1.5) + 2(3)(4.5) + 2(1.5)(4.5)
Surface Area = 6 + 27 + 13.5
Surface Area = 46.5 square inches
Since the redesigned cereal box is a cube, all sides have equal length. Let's call this length x. The surface area of the cube is then:
Surface Area = 6x^2
Set the surface area of the cube equal to the original surface area:
6x^2 = 46.5
x^2 = 46.5 / 6
x^2 = 7.75
x = sqrt(7.75)
x ≈ 2.78 in
Therefore, the length of each side in the cube would be approximately 2.78 in. The closest option provided is 2.9 in.