A cube has side length 3 inches. A sphere has a radius of 3 inches.
a. before any calculations, predict which solid has greater surface area to volume ratio.
b. calculate the surface are, volume, and surface area to volume ratio for each solid.
a. Before any calculations, the sphere is expected to have a greater surface area to volume ratio compared to the cube. This is because spheres have a higher surface area to volume ratio than cubes.
b.
Cube:
Surface Area = 6 * (side length)^2 = 6 * (3)^2 = 6 * 9 = 54 square inches
Volume = (side length)^3 = 3^3 = 27 cubic inches
Surface Area to Volume Ratio = 54/27 = 2 square inches per cubic inch
Sphere:
Surface Area = 4 * pi * (radius)^2 = 4 * pi * (3)^2 = 4 * 3.14 * 9 = 113.04 square inches
Volume = (4/3) * pi * (radius)^3 = (4/3) * 3.14 * (3)^3 = (4/3) * 3.14 * 27 = 113.04 cubic inches
Surface Area to Volume Ratio = 113.04/113.04 = 1 square inch per cubic inch
Therefore, the cube has a surface area to volume ratio of 2 square inches per cubic inch, while the sphere has a surface area to volume ratio of 1 square inch per cubic inch. As predicted, the sphere has a greater surface area to volume ratio compared to the cube.