Concept Byte: Exploring Similar Solids

Use With Lesson 11-7

TECHNOLOGY

To explore surface areas and volumes of similar rectangular prisms, you can set up a spreadsheet like the one below. You choose the numbers for length, width, height, and scale factor. The computer uses formulas to calculate all the other numbers.

Activity

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In cell E4, enter the formula = 2 * ( B 4 * C 4 + B 4 * D 4 + C 4 * D 4 ) . equals 2 times open cap b 4 times cap c 4 plus cap b 4 times cap d 4 plus cap c 4 times cap d 4 close .  This will calculate the sum of the areas of the six faces of Prism I. In cell F4, enter the formula = B 4 * C 4 * D 4 . equals cap b 4 times cap c 4 times cap d 4 .  This will calculate the volume of Prism I.

In cells B5, C5, and D5 enter the formulas = G 4 * B 4 , = G 4 * C 4 , equals cap g 4 times cap b 4 comma equals cap g 4 times cap c 4 comma  and = G 4 * D 4 , equals cap g 4 times cap d 4 comma  respectively. These will calculate the dimensions of similar Prism II. Copy the formulas from E4 and F4 into E5 and F5 to calculate the surface area and volume of Prism II.

In cell H4 enter the formula = E 5 / E 4 equals cap e 5 slash cap e 4  and in cell I4 enter the formula = F 5 / F 4 . equals cap f 5 slash cap f 4 .  These will calculate the ratios of the surface areas and volumes.

Investigate In row 4, enter numbers for the length, width, height, and scale factor. Change the numbers to explore how the ratio of the surface areas and the ratio of the volumes are related to the scale factor.

Exercises

State a relationship that seems to be true about the scale factor and the given ratio.

1. the ratio of volumes
2. the ratio of surface areas

Set up spreadsheets that allow you to investigate the following ratios. State a conclusion from each investigation.

3. the volumes of similar cylinders
4. the lateral areas of similar cylinders
5. the surface areas of similar cylinders
6. the volumes of similar square pyramids

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