Dimensions of cone with smallest volume that can hold a cylinder

In summary, by substituting the given values for height and radius into the cylinder volume equation, the volume of the cylinder is calculated to be 20,357mm^2. Upon using this value to create an equation in terms of height and substituting it into the cone formula, the resulting dimensions for the cone are a radius of 18mm and a height of 135mm. However, it is noted that this answer did not work out when tested.
  • #1
chung963
3
0

Homework Statement


A cylinder of height 45mm and radius 12mm is placed inside a circular cone.
What are the dimensions of the cone with the smallest volume to enclose this cylinder


Homework Equations


v=1/3(pi)r^2h
v=(pi)r^2h
SA=2(pi)rh

The Attempt at a Solution


I substuted values into the cylinder equation and got 20,357mm^2 volume of cylinder and made an equation in terms of h and substitued into the cone formula but answer didnt work out.
Final answer is r=18 and h=135
 
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  • #2
Please post your detailed calculations. Generic descriptions of what you tried aren't very helpful.
 

FAQ: Dimensions of cone with smallest volume that can hold a cylinder

What are the dimensions of the smallest cone that can hold a cylinder?

The dimensions of the smallest cone that can hold a cylinder depend on the dimensions of the cylinder. In general, the cone should have a base that is slightly larger than the base of the cylinder and a height that is equal to the height of the cylinder.

How do you calculate the volume of a cone?

The formula for calculating the volume of a cone is V = 1/3 * π * r2 * h, where r is the radius of the base and h is the height of the cone. You can also use online calculators or software programs to easily calculate the volume.

What is the relationship between the volume of a cone and the volume of a cylinder it can hold?

The volume of a cone and the volume of a cylinder it can hold are directly proportional. This means that as the volume of the cone increases, the volume of the cylinder it can hold also increases, and vice versa.

Can a cone with a smaller base hold a cylinder with a larger base?

No, a cone with a smaller base cannot hold a cylinder with a larger base. The base of the cone must be slightly larger than the base of the cylinder in order for the cylinder to fit inside the cone.

Are there any real-life applications for finding the dimensions of a cone that can hold a cylinder?

Yes, this concept has many real-life applications. For example, it can be used in engineering and construction to determine the size and dimensions of containers or structures that need to hold cylindrical objects. It can also be used in packaging design to ensure that cylinders can fit snugly inside cone-shaped packages.

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