Answer:
When the length of the side of the cube is doubled, the area increases by a factor of four while the volume increases by a factor of eight.
Step-by-step explanation:
Surface area of a cube is given by the formula below:
Surface area of a cube = 6a²
Volume of a cube is also given by the formula below:
Volume of a cube = a³
Where a is the length of a side of the cube.
For the first cube, a = 2 cm
Surface area of the first cube = 6 * (2 cm)² = 24 cm²
Volume of the first cube = (2 cm)³ = 8 cm³
When the side length of the cube doubles, a = 4 cm
Surface area of the second cube = 6 * (4 cm)² = 96 cm²
Volume of the first cube = (4 cm)³ = 64 cm³
The ratio of the area and volume of the new cube is given below:
Area = 96 cm² / 24 cm² = 4
Volume = 64 cm³ / 8 cm³ = 8
Therefore, when the length of the side of the cube is doubled, the area increases by a factor of four while the volume increases by a factor of eight.