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?
Accepted Solution
A:
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