Tom has a rectangular prism-shaped suitcase that measures 9 inches by 9 inches by 24 inches. He needs a second suitcase that has the same volume but a smaller s

Question

Tom has a rectangular prism-shaped suitcase that measures 9 inches by 9 inches by 24 inches. He needs a second suitcase that has the same volume but a smaller surface area than his current suitcase. Which suitcase size would fit Tom’s needs?

 

A: 18 inches by 18 inches by 6 inches

 

B: 12 inches by 10 inches by 9 inches

 

C: 16 inches by 5 inches by 9 inches

 

D: 18 inches by 9 inches by 12 inches

Answer 1

9x9x24 = Volume of 1944 cubic inches

It has surface area of 2(81) + 4(216) = 162+864 = 1026 square inches

1944 ends in a digit 4

A and D end in 4

C and B dont' have 1944 for volume

A or D might. Both look like they have 1944 for volume.

A has area 2(18)^2 + 4(18)(6) =

D has 2(18(9) + 2(18)(12 + 2(9)(12)= more area than A

A's area = 2((18)^2 + 2(18)(6) = 648+216 = 864 square inches

D's area = 18^2 + 18(24) + 18(12) = 18(18+24+12) = 54(18) = 972

A has same volume and least surface area