3. A container in the shape of a right circular cylinder with no top has surface area 3n ft2. What height h and base radius r will maximize the volume of the cylinder?

College Algebra (MindTap Course List)
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ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
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Activity 2.
Let's Optimize!
Directions: Solve the problems below. Show your complete solutions.
1. An open-top box is to be made from a 24 in. by 36 in. piece of cardboard
by removing a square from each corner of the box and folding up the flaps
on each side. What is the maximum volume of the box?
2. If 1000 cm2 of cardboard is available to make a box with a square base,
find the largest possible volume of the box.
3. A container in the shape of a right circular cylinder with no top has
surface area 3n ft2. What height h and base radius r will maximize the
volume of the cylinder?
Transcribed Image Text:Activity 2. Let's Optimize! Directions: Solve the problems below. Show your complete solutions. 1. An open-top box is to be made from a 24 in. by 36 in. piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. What is the maximum volume of the box? 2. If 1000 cm2 of cardboard is available to make a box with a square base, find the largest possible volume of the box. 3. A container in the shape of a right circular cylinder with no top has surface area 3n ft2. What height h and base radius r will maximize the volume of the cylinder?
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