Student Page for Using Diameter, Volume and Surface Area to Determine
the Dimensions of PSA's Computer
Introductory video
The Main Problem:
NASA needs you to design a computer for the Personal Satellite Assistant,
a robot helper that will assist the astronauts in space. This robot
is shaped like a sphere and has a diameter of 8 inches. The computer
must meet the following criteria:
 a rectangular prism with a volume of 24 cubic inches
 must fit inside a sphere with a diameter of 8 inches
 must have the largest possible surface area to allow the computer to easily
release heat so that it doesn't overheat
Main
Problem video
Prerequisites:
 What is diameter?
 What is diameter of a sphere?
 How do you calculate volume?
 What is surface area?
 How do you calculate surface area?
Prerequisites
video
 Multiplying and dividing decimals.
 A rectangular prism is a three dimensional
solid with six rectangular faces.
 A sphere is a round threedimensional
solid with all points of the surface at the same distance from
the center.
Materials:
For each group:
 24 oneinch cubes
 1 paper circle with an 8inch diameter
 graph paper
 1 calculator per student
Procedure
 Use your materials to find solutions to your problem.
 Check that
each solution meets the criteria in the problem.
 Questions
to consider as you look for solutions:
 How many possible solutions
do you think there are?
 Does a solution have to have all whole
numbers for the volume dimensions?
 How small does the width of
the computer need to be to fit within the curvature of
the sphere so that no corners stick out?
 What causes surface area to increase?
 What shapes have the greatest
surface area?
 As the height of the computer decreases, what happens
to the surface area?
 How do you know that your answer is the
best answer?
 Write a letter to NASA with your recommendation
of the dimensions the computer should be, how you figured it
out and why you think it's the best answer.
Extension Problem
NASA’s robot also uses fans to move around in microgravity. These
fans are shaped like cylinders. The cylinders also need to have the maximum
surface area in order to release heat. Should NASA use short and fat
cylinder fans or long and skinny cylinder fans? Explain your answer.
Extension
Problem video
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