Question

PLEASE HELP!!!!
A rectangular prism has the following dimensions.

length: 18 inches

width: 1 foot

height: 14 inches

If all the dimensions of this prism are tripled, what will be the surface area of the new figure?

3,816 in.^
7,632 in.^
27,216 in.^
11,448 in.^

Answer 1

The surface area of a rectangular prism is just the area of all the faces added together. You have six faces. The area of them are as follows: \(2lw\), \(2wh\), \(2lh\).

So, you have that the total surface area of the rectangular prism is: \(2lw+2wh+2lh\). If the dimensions are tripled, then \(l=3a\), \(w=3b\), and \(h=3c\) (where a is your original length, b is your original width, and c is your original height).
So we have:
\(2lw+2wh+2lh=2(3a)(3b)+2(3b)(3c)+2(3a)(3c)=18ab+18bc+18ac\)

Since \(a=18 \text{ in}\), \(b=1 \text{ ft }=12 \text{ in}\), and \(c=14 \text{ in}\).

So, the total surface area is: \(18(18\text{ in})(12 \text{ in})+18(12 \text{ in})(14 \text{ in})+18(18 \text{ in})(14 \text{ in})=11,448 \text{ in}^2\)

You can also think of it this way:

Apply the original formula \(2lw+2wh+2lh\) after multiplying your original length, width, and height by \(3\).

Answer 2

thanks!

Answer 3

You're welcome.