Conclusions:
• The maximum volume for a given surface area of a square­based prism always occurs when the prism is a ___________.
• The surface area of a cube is given by the formula ___________, where is the side length of the cube.
• When you are given the surface area, solve for s to find the dimensions of the square­based prism with maximum volume.
Maximize the Volume of a Square‐Based Prism
When restricted by the amount of material you have to finish a job, it is important to be able to determine
the greatest possible volume from the available material.
Example 1: a) Determine the dimensions of the square­based prism with maximum volume for a surface area of 2400 m2. Round to the nearest tenth of a unit.
Investigation: a) Each of the square­based prisms has a surface area of 24 cm2. Calculate the area of the
base and the volume of each prism. Record your data in a table.
b) Which square­based prism has the maximum volume? Describe the shape of this prism compared to the others.
b) Determine the volume of the prism, to the nearest cubic unit.
Homework: Pg. 501: #1, (2, 3) ad, 5, 7, 8