If you are provided with a cube of modeling clay, which of the following changes to the shape of this cube will decrease its surface area relative to its volume?

Question

Cut the cube into eight smaller cubes.
Stretch the cube into a long, shoebox shape.
Flatten the cube into a pancake shape.
Round the clay up into a sphere.

Answer 1

To determine which change will decrease the surface area relative to volume, we can analyze each option.

1. Cut the cube into eight smaller cubes: Cutting the cube into eight smaller cubes will increase the overall surface area. Each smaller cube retains its total volume, but the total surface area of eight smaller cubes is greater than that of one larger cube.

2. Stretch the cube into a long, shoebox shape: Stretching the cube into a shoebox shape typically increases the surface area per unit of volume. The surface area increases significantly compared to the rectangular volume formed, leading to a higher surface area-to-volume ratio.

3. Flatten the cube into a pancake shape: Flattening the cube into a pancake shape increases the surface area relative to its volume since the height decreases while the surface area on the sides increases.

4. Round the clay up into a sphere: When a shape is transformed into a sphere, the surface area-to-volume ratio decreases. A sphere has the lowest surface area for a given volume when compared to other shapes. This means that rounding the clay into a sphere will reduce its surface area relative to its volume.

Therefore, the change that will decrease the surface area relative to its volume is:

Round the clay up into a sphere.