Solving the Cylinder Volume Problem

  • Context: High School 
  • Thread starter Thread starter Paradiselovek
  • Start date Start date
  • Tags Tags
    Cylinder Volume
Click For Summary
SUMMARY

The discussion focuses on solving the cylinder volume problem where a soup company increases the height of its can by 30% while maintaining the same volume. The formula for the volume of a cylinder, V = πr²h, is utilized to establish the relationship between the original dimensions (height h and radius r) and the new dimensions (height h* = 1.3h and radius r*). The key conclusion is that the radius must be decreased to maintain volume, and the percentage change in radius can be calculated using the formula (r* - r)/r, which simplifies the problem significantly.

PREREQUISITES
  • Understanding of the volume formula for a cylinder (V = πr²h)
  • Basic algebra skills for manipulating equations
  • Knowledge of percentage calculations
  • Familiarity with geometric concepts related to cylinders
NEXT STEPS
  • Study the derivation and application of the cylinder volume formula (V = πr²h)
  • Learn how to manipulate algebraic equations to solve for unknown variables
  • Explore percentage change calculations in various mathematical contexts
  • Investigate real-world applications of volume calculations in packaging design
USEFUL FOR

Students studying geometry, engineers involved in product design, and anyone interested in mathematical problem-solving related to volume and dimensions.

Paradiselovek
Messages
9
Reaction score
0
please help me thank you so much ^^(I need help quick before the due date thanks)

Here the problem:

A soup company decides to increase the height of its can by 30% but to maintain their present volume. To the nearest percent, how much must the radius of the can be decreased to hold the volume constant.

(there a picture of the can which is a plain cyclinder)

I try working backward for the equation to find the volume of a cyclinder, but i really don't know if I got that right. please help me
 
Physics news on Phys.org
What's the formula for the volume of a cylinder? Let's use h for the original height and r for the original radius of the can, and h* and r* for the new height and radius. The basic set up is

old volume = new volume

where h* = 1.3 h. Just plug this into the equation and solve for r*. Your answer will depend on r, of course.

Then find the percentage change: (r* - r)/r . The r's will cancel out at this step.
 

Similar threads

High School How to draw a plane intersecting a cylinder at a "compound angle"
  • · Replies 8 ·
Replies
8
Views
3K
High School Volume of paraboloid in a cylinder
  • · Replies 2 ·
Replies
2
Views
3K
High School Need some clarification to get dimensions for a volume
  • · Replies 5 ·
Replies
5
Views
2K
The volume of a "spherical cap" using triple integrals
  • · Replies 9 ·
Replies
9
Views
3K
Maintaining Volume in a Cylinder: Solving for the Necessary Radius Adjustment
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Geometry Problem: Show Area & Volume of Sphere & Cylinder
  • · Replies 1 ·
Replies
1
Views
2K
Trying to resolve a volume calculation
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Warm-up time for a hollow cylinder
  • · Replies 5 ·
Replies
5
Views
3K
Optimization problem - right circular cylinder inscribed in cone
  • · Replies 9 ·
Replies
9
Views
5K
High School The distance to the nearest identical Hubble volume in light years?
  • · Replies 50 ·
2
Replies
50
Views
8K