Question

If the dimensions of a solid proportionally increase by a scale factor of 5, by what factor does the surface area

increase?
n/a n/t
0 $
O
25
O 25

Answer 1

If the dimensions of a solid proportionally increase by a scale factor of 5, the surface area increases by a factor of 25.

Step-by-step explanation:

If the dimensions of a solid proportionally increase by a scale factor of 5, the surface area increases by a factor of 25.

To understand this, let's consider a cube. The surface area of a cube is given by 6a², where a is the length of one side of the cube. If we increase the dimensions of the cube by a scale factor of 5, the new length of one side becomes 5a. So, the new surface area is 6(5a)² = 150a².

Comparing the new surface area (150a²) with the original surface area (6a²), we can see that the new surface area is 25 times greater than the original surface area (150a²/6a² = 25).

Learn more about surface area