Question

We can experiment with two parallelepipeds (boxes) that are similar in shape. The dimensions of the smaller box are 2 in. x 4 in. 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 six sides. 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 small box

2. Compare the volumes (V) of the two boxes, measured in cubic inches. 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 the box. 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 the large box is ___ times the volume of the small box.

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

	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 of thatch for the kibo Art Gallery. Do you agree with it? Explain.

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

Answer 1

1) Ratio: SA of the large box is 4 times the SA of the small box

2)Small box _8_ cubes fill one layer, and 3 layers fill the box. The box holds _24__ 1-inch cubes. Volume= __24__ cu. in. Large box __32_ cubes fill one layer, and _6_layers fill the box The box holds __192__ 1-inch cubes. Volume= _192__ cu. in. Ratio: The volume of the large box is _8__ times the volume of the small box.

3) see in the 3rd image