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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?

User Ishaq Khan
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1 Answer

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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.

User Dave Goodell
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