Math

Question

What is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 432 cm2?

Answer 1

Let the missing length be x. The surface area of a rectangular prism is given by the formula: SA = 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height respectively.

We are given the surface area (SA) as 432 cm², the width (w) as 9 cm, and the height (h) as 9 cm. We can plug these values into the formula and solve for the missing length (l):

432 = 2(9)(l) + 2(9)(9) + 2(9)(9)

432 = 18l + 162 + 162

Now combine the constants:

432 = 18l + 324

Subtract 324 from both sides:

108 = 18l

Now divide by 18 to find the length:

6 = l

So the missing length of the rectangular prism is 6 cm.