Question

For a rectangular prism, if the base length was shrunk by a factor of two-thirds, the width was quadrupled, and height was cut in half, how would the changes affect the surface area formula? The attachment has the problem and the answer choices. Thanks.

Answer 1

Surface area = 2(wl + hl + hw) = 2wl + 2hl + 2hw

Conditions:
base length is shrunk by a factor of 2/3
width is quadrupled
height is cut in half.

l ⇒ 2l/3 w ⇒ 4w ; h ⇒ h/2

SA = 2wl + 2hl + 2hw
SA = 2(4w)(2l/3) + 2(h/2)(2l/3) + 2(h/2)(4w)
SA = (16wl/3) + 4hl/6 + 8hw/2

Simplify:

SA = 16/3 wl + 2/3 hl + 4hw   Choice C.