MATH SOLVE

2 months ago

Q:
# 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

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