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?
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2.3 inches
2.5 inches
3.5 inches
4 inches
To find the surface area of the cereal box, we calculate the sum of the areas of each face:
2(3*1) + 2(3*4) + 2(1*4) = 6 + 24 + 8 = 38 sq in
Since a cube has all sides equal, if it has a surface area of 38 sq in, we can find the length of each side by solving for s in the equation for the surface area of a cube:
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 would be approximately 2.5 inches.
For the two designs in question above, which one holds more volume?
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the rectangular prism with dimensions of 3 in. x 1 in. x 4 in.
the cube with a side length from the answer above
To compare the volumes of the two shapes, we first need to calculate the volume of each shape.
For the original rectangular prism:
Volume = length x width x height = 3 x 1 x 4 = 12 cubic inches
For the cube with a side length of approximately 2.52 inches:
Volume = side length^3 = 2.52^3 ≈ 16 cubic inches
Therefore, the cube holds more volume (16 cubic inches) compared to the original rectangular prism (12 cubic inches).