7. 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 3.2 in 3.2 in 2.9 in 2.9 in 2.2 in 2.2 in 6.4 in
To find the surface area of the cereal box, we can use the formula for the surface area of a rectangular prism:
Surface Area = 2lw + 2lh + 2wh
Given dimensions: l = 3 in, w = 1.5 in, h = 4.5 in
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 box is a cube with the same surface area, the surface area of a cube is given by the formula 6s^2, where s is the length of each side of the cube.
6s^2 = 46.5
s^2 = 46.5/6
s^2 = 7.75
s = sqrt(7.75)
s ≈ 2.78 in
Therefore, the length of each side in the cube would be approximately 2.8 inches. The closest response option is 2.9 in.