We can experiment with two parallelepipeds (boxes) that aresimilar in shape. The dimensions of the smaller box are 2 in. x 4in. x 3 in. The larger box has twice the dimensions of the smaller. Draw and label the large box

1. Surface area (SA) of a box is the sum of the areas of all sixsides. Compare the SAs of the two boxes.

	top or bottom	front or back	side	total surface area
Small box	2x4= 8 in sq.	3x4=12 in sq.	2x3= 6 in sq.	2(8+12+6)=52 in. sq.
Large Box

Ratio: SA of the large box is ___ times the SA of the smallbox

2. Compare the volumes (V) of the two boxes, measured in cubicinches. Pretend that you are filling the boxes with 1-inch cubes.The volume of each cube is 1 cubic inch (cu. in.).

Small box ____ cubes fill one layer, and ___ layers fill thebox. The box holds ___ 1-inch cubes. Volume= ____ cu. in. Large box___ cubes fill one layer, and ___ layers fill the box The box holds____ 1-inch cubes. Volume= ___ cu. in. Ratio: The volume of thelarge box is ___ times the volume of the small box.

3. Show your work to compare a 3inch cube with a I-inchcube.

	large cube	small cube	ratio: large to small
length of side	3 in.	1 in.	3 to 1
surface area
volume

Think about this: 1. Look at your estimate for the amount ofthatch for the kibo Art Gallery. Do you agree with it? Explain.

2. Two cylinders (cans) have similar shapes. One has four timesthe dimensions of the other. Show how you can compare their surfaceareas and volumes without the use of formulas. What conclusions doyou expect? Use another sheet, if necessary.