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.
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.
1 answer
2 answers