Time
for MATH MINUTE! (provide your favorite theme music here).
Get
out your paper & pencil because I have a new puzzle for you!!
PUZZLE #33 Surface
and volume Sept.
10-14
In
Puzzle 31 we saw that two rectangles can have the same perimeter but different
areas.
What
about solids you ask? Can two solids have the same surface area but different
volumes or vice versa?
Try
this calculation:
Take
a box of size 1x2x4, a cube of size 2x2x2 and a sphere of radius r = 1.382 (all
measurements in inches).
Compute
the surface area of each and the volume of each*.
Which
one has the largest surface area? smallest surface area?
Which
one has the largest volume? smallest volume?
*For the box remember you have a top and bottom, front and
back, and two ends, but for the cube all sides are equal (how many are there?).
The volume of the box is the length times the width times the
height, but for the cube you can cube the size of the side (is this why they
call it a cube?).
The surface area of a sphere is (4pi)r2 and the
volume is (4pi)r3/3.
Send
your comments, ideas and solutions before Monday to this email address, and be sure to
put MM in the subject line: parksjm@potsdam.edu
Visit
us here online to see the results every Monday.
See
you next time on MATH MINUTE! (theme music fades out here).