7th Grade Math

Lesson 2D Surface Area 593

and Apply

Compare the two figures that have the same volume. Then determine which

one has a greater surface area. Explain.

6.

6 ft

2 ft

7 ft

'JHVSF


7 ft

3 ft

4 ft

'JHVSF


7.

7 m

4 m

'JHVSF


(^) 2 m 28 m
'JHVSF


8. PACKAGING Chandler wants to build a box that will hold as many of his
   collector’s coins as possible. He wants the volume of the box to be 20 cubic
   inches. The dimensions of possible boxes are given in the table below. Find
   the surface area of each box. Then determine which box has the least
   amount of surface area.

Box () (w)

1

2

3

4

20

4

2

10

1

5

2

2

1

1

5

1

20

20

20

20

Surface

Area

Volume

(in^3 )

(h)



w

h

9. CRAFTS Monique sews together pieces of fabric to make gift boxes. If she
   only uses whole numbers, what are the dimensions of a box with a volume
   of 50 cubic inches that has the greatest amount of surface area?


10. CONTAINERS Thomas is creating a decorative container to fill with colored
    sand. What will be the dimensions of the rectangular prism that will hold
    100 cubic inches with the least amount of surface area, if he only uses whole
    numbers? The top of the container is open.


11. BOXES The specifications of a cardboard box indicate that it has the same
    volume as a rectangular box 4 inches by 10 inches by 12 inches, but with
    less surface area. What size box would meet these requirements?


12. COOKING Zachariah needs to melt a stick of butter 5 inches by 1 inch by
    1 inch in a pan. Explain why cutting the butter into smaller pieces will help
    the butter melt faster.

592_599_C10_L2_895130.indd 593 1/4/10 2:55 PM