Superlesson
Project 9-2

Geometry

Chapter 9, Surface Area and Volume

Superlesson 9-2, Volume

Many naturally occurring objects have shapes which may be approximated by simple three-dimensional figures such as prisms, cylinders, cones and spheres. Because we know how to find the volumes of such figures, this gives us an easy method to estimate the volumes of many objects in nature.

Part A, Volume of Prisms

1. Go to Mother Nature's tile floor Web site to see a picture of the top of Devil's Postpile.

a.Read the description of this amazing natural formation. It is composed of many vertical shafts, some shaped like regular hexagonal prisms. What is the approximate diameter of each of these shafts?

b. To see a front view of Devil's Postpile, go to this Web site.

c. Find the approximate height of Devil's Postpile in the first paragraph of the Devil's Postpile Reds Meadow Web site.

d. Assuming that the "diameter" in 1a is drawn as in the figure below, find the approximate volume of one of the vertical columns with a hexagonal base in Devil's Postpile.

Part C, Volume of Cylinders and Cones

2. Use the Internet to answer the following questions.

a. The trunk of a tree can be approximated by a cylinder. Go to the Coast Redwood Primer Web site to see some information about the coast redwoods. What is the approximate radius of the base of "Tall Tree?"

b. Find the approximate volume for the trunk of "Tall Tree," the tallest coast redwood anywhere.

c. Do you believe your approximation is greater or less than the actual volume of the trunk of "Tall Tree?"

3. Volcanoes are approximately conical in shape. Go to the Mount Shasta Volcano Web site to see information from various sources about Mount Shasta, a volcano in northern California. For this project, use the information given by Wood and Kienle (1990), the fourth source from the top.

a. What is the height from the base of Mount Shasta to its top in kilometers? What is its approximate volume?

b. Use the information in 3a to find the approximate circumference of the base of Mount Shasta.

c. Why is it important to know the volume of a volcano?

Part D, Surface Area and Volume of Spheres

4. Spheres are good approximations for the shapes of both the Earth and the Moon. Go to the Earth Web site to get dimensions for both the Earth and the Moon. How many times bigger is the Earth's volume than the Moon's?