Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Learning Math Home
Measurement Session 9: Solutions
Session 9 Part A Part B Part C Homework
measurement Site Map
Session 9 Materials:

A B C 


Solutions for Session 9 Homework

See solutions for Problems: H1 | H2 | H3 | H4 | H5

Problem H1

Dinosaurs' plates were likely the result of their very low surface area-to-volume ratio: The plates served to increase the dinosaurs' surface area without increasing their volume very much.

Animals with a great deal of surface area but little volume cool down and heat up faster than animals with larger volumes. This is important in reptiles since they obtain their body heat from the sun.

<< back to Problem H1


Problem H2


The minimum surface area occurs when the height is exactly twice the radius. If the volume is 500 cm3, the radius is approximately 4.30 cm, while the height is approximately 8.61 cm.


In this shape, the can fits perfectly inside a cube, since the diameter of the can is the same as the height. Some cans are made in this shape. When cans are displayed in stores or placed on shelves, there is often more of a premium on radius (shelf space), so the radius is often smaller than our "ideal" can.

<< back to Problem H2


Problem H3

One obvious way is to increase the surface area-to-volume ratio of the tablet. It would dissolve more quickly. A flat caplet dissolves more quickly than a spherical pill.

<< back to Problem H3


Problem H4

This is the same type of problem as the "area of the hand" problem in Problem A7. The answer depends on the shape of the rectangle Mr. Hobbs used, since different rectangles with the same perimeter will have different areas. There is no way of guaranteeing that, using this method, the area of the two figures would be the same.

<< back to Problem H4


Problem H5

Yes, a similar ratio exists. The ratio for spheres is r:3 rather than s:6 for cubes and can most easily be found by using a table or by dividing the two formulas into one another.

<< back to Problem H5


Learning Math Home | Measurement Home | Glossary | Map | ©

Session 9 | Notes | Solutions | Video


© Annenberg Foundation 2017. All rights reserved. Legal Policy