If a cubical cell with 2-cm sides doubles the dimensions of its sides, what relative change occurs to the ratio of its surface area to volume ratio?

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.

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.

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