Question

A rectangular prism has side lengths of 4 inches, 6 inches, and 7 inches. If all side lengths are multiplied by 5, what happens to the surface area. A) It remains the same. B) It is multiplied by 5. C) It is multiplied by 25. D) It is multiplied by 125.

Answer 1

C

Explanation:

The surface are of the prism will be the area of a each side added together. The work would look like this:

SA = 2[(l×h)+(l×b)+(b×h)]

SA = 2(lh+lb+bh)

But if you multiply each dimension by 5, the area becomes

SA = 2[(5l×5h)+(5l×5b)+(5b×5h)]

SA = 2(5²lh+5²lb+5²bh)

SA = 5²×2(lh+lb+bh)

SA = 5²area

Since 5² = 25, then the the surface area is multiplied in size by 25.