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Trigonometry and Calculus: Volume
The concept of volume is important at all levels of mathematics.
Some of the volume problems below, such as
The SuperUltraMegaBig
Cup, are more easily solved by using calculus. Others, like
That's A Lot of Rock,
can be solved by using area and volume formulas.
For background information elsewhere on our site, explore the
High School Trigonometry
and Calculus
areas of the Ask Dr. Math archives. To find relevant
sites on the Web, browse and search
Trigonometry and
Calculus (Single Variable)
in our Internet Mathematics Library.
Access to these problems requires a Membership.

Building Boxes
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the maximum volume of a rectangular prism constructed from an 8.5inch by 11inch piece of paper.
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Cup Capacity
 Leigh Nataro

Trig/Calc, difficulty level 3. Find the volume of a cup based on its dimensions.
... more>>

Doughnut Dilemma
 Leigh Nataro

Trig/Calc, difficulty level 2. Which doughnut shop makes a doughnut with a greater volume?
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Five Golden Rings
 Leigh Nataro

Trig/Calc, difficulty level 5. Based on the given information, find the volume of five golden rings.
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The General Box Company
 Leigh Nataro

Trig/Calc, difficulty level 3. A rectangular piece of cardboard is folded up to make a box. Find a general formula for the maximum volume of the box.
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Googol the Giant's Gargantuan Goblet
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the volume of Googol the Giant's elliptical paraboloid goblet.
... more>>

Job Interview at the CanCan Company
 Leigh Nataro

Trig/Calc, difficulty level 3. Find the smallest amount of tin needed to make a can that can hold 12 cubic inches.
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Shipping Packages
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the maximum volume of a box based on the given information.
... more>>

The SuperUltraMegaBig Cup
 Alvirne High School Calculus Class

Trig/Calc, difficulty level 3. What is the minimum cost to make a cup based on given information?
... more>>

That's A Lot of Rock!
 Leigh Nataro

Trig/Calc, difficulty level 3. Find the volume of a tunnel through a mountain.
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Time to Make the Doughnuts
 David Turner

Trig/Calc, difficulty level 4. Find the radius of a doughnut with center at (0, 10) and a volume of 3158 cubic centimeters.
... more>>

Your Interview Question Is...
 Leigh Nataro

Trig/Calc, difficulty level 3. If you want to minimize the surface area of a can with a fixed volume, what should be the ratio of the height to the radius?
... more>>
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