Question

What is the percent of change in surface area for a cube-shaped cell that grows from 1 cm to 3 cm on each side?

A) 50%
B) 100%
C) 200%
D) 300%

Answer 1

The percent change in surface area for a cube-shaped cell that grows from 1 cm to 3 cm on each side is calculated using the formula for surface area of a cube. Initially, the surface area is 6 cm², and after growth, it is 54 cm², resulting in an 800% increase in surface area.

Step-by-step explanation:

To determine the percent change in surface area for a cube-shaped cell that grows from 1 cm to 3 cm on each side, we need to calculate the surface area for both the original and new size of the cube and then find the percent change between them.

The surface area (SA) of a cube is given by the formula SA = 6s², where 's' is the length of one side of the cube.

For the smaller cube with a side length of 1 cm:

• SA = 6(1 cm)² = 6 cm²

For the larger cube with a side length of 3 cm:

• SA = 6(3 cm)² = 54 cm²

Now, we calculate the percent change using the formula: Percent Change = (New SA - Original SA) / Original SA × 100%

Percent Change = (54 cm² - 6 cm²) / 6 cm² × 100%

Percent Change = (48 cm²) / 6 cm² × 100%

Percent Change = 800%

Therefore, the correct answer is that the percent change in surface area for the cube-shaped cell is 800%.