Similar Solids
Pacing:This lesson should take one to two class periods
Goal:This lesson introduces students to the surface area and volume formulas of cones.
Gulliver’s Travels Revisited!In a previous lesson, we connectedGulliver’sTravels to areas of similar figures, such
as the footprints of Gullivers versus the Lilliputians. Extend this topic to surface area and volume.
The surface area (amount of material needed to make clothing, etc.) has a ratio
(
image area
preimage area)
ofk^2. Therefore, ifa Lilliputian was 121 the size of Gulliver and Gulliver was 121 the size of a Brobdignagian, the amount of material
needed to cloth a Brobdignagian would be 144^2 times the amount needed for a Lilliputian!
This also related to volume (weight). The ratio here would bek^3. Have fun and try lots of different ratios!
1.11. Surface Area and Volume