Question

Sara is wrapping gift boxes. Each gift box is a rectangular prism with a square base of side 6 inches. The difference between the heights of the two gift boxes is 3 inches.

If the larger box has a surface area of 216 square inches, what is the difference in the surface area of the two boxes?

108 square inches

72 square inches

36 square inches

18 square inches

Answer 1

@jim_thompson5910

Answer 2

@dpaInc

Answer 3

i think im doing something wrong because i got 144

Answer 4

The base is 6^2 = 36 square inches

So the area of the two bases combined is 2*36 = 72 square inches

Answer 5

The larger box has a surface area of 216 sq inches, so it has a lateral surface area of 216 - 72 = 144 square inches

Answer 6

You can then use this lateral surface area to find the height of the larger box

Answer 7

6?

Answer 8

therefore it is...72?

Answer 9

good, so the smaller box has a height of 3 inches (since the larger box is taller by 3 inches)

Answer 10

yeah

Answer 11

the lateral surface area of the smaller box is then....

Answer 12

72 right? because 24*3

Answer 13

yep, so the total surface area of the smaller box is

72 + 72 = 144

you add the base area (72) and the lateral surface area (72) to get 144

Answer 14

the difference of the two surface areas is then

Big - Small = 216 - 144 = 72

Answer 15

ohhh i actually didnt read the question properly

Answer 16

i thought the question was asking what the area of the smaller one was

Answer 17

ok thanks

Answer 18

alternatively, you can draw out the two boxes, then just focus on the upper half of the larger box that has a height of 3

and if you just focus on the lateral surface area and unfold it out, you'd get this

Answer 19

and you'd get the area to be 3*24 = 72 square inches

Answer 20

ok thx

Answer 21

so answer is B right? just double checking..

Answer 22

yep