geometry-labs

LAB 10.5
3-D Blowups (continued)
Name(s)
3. Repeat Problem 2 with a scaling factor of 3. Use even fewer cubes in the
smaller solid!
Surface area
Volume
Original Blowup Ratio Original Blowup Ratio
4. Choose one of the solids in the figure below, different from your neighbors’
choices.Without using physical cubes, find the surface area and volume for
blowups of your solid, and fill out the table.You may use sketches.
Scaling Surface Area Volume
factor area ratio Volume ratio
1
2
3
4
5
6
Discussion
A. When you use a scaling factor k, what happens to each individual unit cube
How does this determine the ratio of surface areas The ratio of volumes Explain.
B. Write a formula for the surface area A of a scaled solid as a function of the
original surface area A 0
and the scaling factor k. Repeat for the volume.
C. Write a formula for the volume V of the blown-up versions of the solid you
studied in Problem 4 as a function of the surface area A and the scaling factor k.
Compare your formula with those of your neighbors.
142 Section 10 Similarity and Scaling Geometry Labs
© 1999 Henri Picciotto, www.MathEducationPage.org