Question

A right rectangular prism is enlarged by a scale factor of 7. What is the ratio of the surface area of the enlarged prism to the surface area of the original prism with a length of 5 inches, height of 4 inches, and a width of 3 inches?

Answer 1

First we look for the surface area of the original rectangular prism.
We have then:
A = 2 * (l * h) + 2 * (l * w) + 2 * (h * w)
Where,
l: length
h: height
w: width
Substituting values:
A = 2 * (5 * 4) + 2 * (5 * 3) + 2 * (4 * 3)
A = 94 in ^ 2
We are now looking for the enlarged prism area:
A '= k ^ 2 * A
Where,
k: scale factor
A: area of the original prism
Substituting values we have:
A '= (7) ^ 2 * (94)
A '= 4606 in ^ 2
The relation of areas is:
A '/ A = 4606/96
A '/ A = 49
Answer:
The ratio of the surface area of the enlarged prism to the surface area of the original prism is:
A '/ A = 49