MTHSC 118
Lab 17: Surface Area & Volume
Name
SN
April 7, 2010
1.
Go to page Pyramid-1. Use spin, pitch, and roll to change your view of the
regular pyramid.
2.
Change the number of sides (N), the size of the base (R), and the slant
height (L). View the pyramid from different angles.
3.
Adjust the controls to look at the pyramid from directly above. Which
control did you use to do this?
What does the pyramid look like in this position?
What does the spin control do now?
4.
Go to page Pyramid-2. Change the size of the base and change the number of
sides. Measure the distance from R to the midpoint of the thick red side.
Label the measurement r.
5.
Measure one side of the base and have Sketchpad calculate the perimeter.
Write down your calculation and results here.
6.
Find the area of the base. Imagine dividing the regular polygon into simpler
shapes and do some measurements and calculations. (If you are stuck, press
Show Hint to get some ideas.) Write down your calculation and result here.
7.
Increase the number of sides to more than 50. Divide the perimeter by r
and divided the area by r2. Have you seen these two numbers before? Why
do you think you get these values?
Adapted from Sketchpad LessonLink
Lab 17: Surface Area & Volume
April 7, 2010
8.
Go to Pyramid-3. Drag L, R, and N. to change the slant height, the size of the
base, and number of sides. Measure the distance r and side length s as you
did in steps 4 and 5. Measure the slant height of the pyramid and label it l.
9.
Find the total area of the lateral faces. Calculate a value that will be correct
for any value of n. Write down your calculation and the result here.
10.
What is the value when the number of faces is a least 50? Why?
11.
Go to page Pyramid-4. Do the necessary constructions, measurements, and
calculations to find the total surface area of the regular pyramid, including
the base and the lateral faces. Write down your calculation and result.
12.
Go to page Prism. Do the necessary constructions, measurements, and
calculations to find the total surface area of the regular prism, including the
base and the faces. Write down your calculation and result.
Adapted from Sketchpad LessonLink
Lab 17: Surface Area & Volume
April 7, 2010
13.
Go to page Perfect Package. Change the dimensions to match those pictured
below. What is the volume and surface area?
14.
Can you find a package that has the same volume, but a different surface
area? Can you find a package with the same surface area, but different
volume? Drag the length, width, and height sliders to see whether you can
come up with examples of such packages. Describe what you found.
Adapted from Sketchpad LessonLink
Lab 17: Surface Area & Volume
15.
April 7, 2010
Find all the ways 24 cubes can be arranged into a package. For each
arrangement write the dimensions and surface area in the table.
Length
Width
Height
Surface Area
Volume
24 cubic units
24 cubic units
24 cubic units
24 cubic units
24 cubic units
24 cubic units
24 cubic units
24 cubic units
Adapted from Sketchpad LessonLink
Lab 17: Surface Area & Volume
April 7, 2010
16.
Which of your arrangements has the least surface area? Which has the
greatest?
17.
For each of the given volumes, which package has the least surface area?
Volume= 8 cubic units
Volume= 12 cubic units
Volume=27 cubic units
Volume=48 cubic units
18.
For each of the given volumes, which package has the greatest surface area?
Volume= 8 cubic units
Volume= 12 cubic units
Volume=27 cubic units
Volume=48 cubic units
19.
For any given volume, describe how you would find the packages with the
least and greatest surface areas.
Adapted from Sketchpad LessonLink