Question

Calculate the surface area, the volume, and the surface-area-to-volume ratio of this cube. SA = height * width * number of sides V = width * length * height Ratio = SA ¸ V: 1

Answer 1

To find the surface area, volume and surface-area-to-volume ratio of a cube, use the formulas SA = 6s² and V = s³. The small cube with side 1 cm has a SA of 6 cm², a V of 1 cm³, and a ratio of 6. The large cube with side 3 cm has a SA of 54 cm², a V of 27 cm³, and a ratio of 2.

Step-by-step explanation:

To calculate the surface area, volume, and surface-area-to-volume ratio of a cube, we will use the provided information for both small and large cubes.

Small Cube:

Side (s) = 1 cm

• Surface Area (SA) = 6s² = 6 * (1 cm)² = 6 cm²
• Volume (V) = s³ = (1 cm)³ = 1 cm³
• Surface-Area-to-Volume Ratio (SA:V) = SA / V = 6 cm² / 1 cm³ = 6

Large Cube:

Side (s) = 3 cm

• Surface Area (SA) = 6s² = 6 * (3 cm)² = 54 cm²
• Volume (V) = s³ = (3 cm)³ = 27 cm³
• Surface-Area-to-Volume Ratio (SA:V) = SA / V = 54 cm² / 27 cm³ = 2

A larger cube has a smaller surface area to volume ratio than a smaller cube.