If the length, width, and height of the rectangular prism are doubled, what would be the surface area of the prism?

Question

a rectangular prism with the messurements being 8m across the bottom, 2m acroos, and 3m going up the back

Answer 1

The surface area would increase by 4.

 

If we let l = 8, w = 2, and h = 3, then the surface area of a rectangular prism is found by:

 

SA = 2(wl + hl + hw)

 

= 2(2 * 8 + 3 * 8 + 3 * 2)

 

= 2(16 + 24 + 6)

 

= 2(40 + 6)

 

= 2(46)

 

= 92 m³

 

Now, let's double the dimensions such that l = 16, w = 4, and h = 6

 

Now, the surface area will be:

 

SA = 2(4 * 16 + 6 * 16 + 6 * 4)

 

= 2(64 + 96 + 24)

 

= 2(160 + 24)

 

= 2(184)

 

= 368 m³

 

368 = 4 * 92