# What is the maximum volume of a cylinder inscribed in a cone?

## What is the maximum volume of a cylinder inscribed in a cone?

The volume of the inscribed cylinder is V = πx^2(h-y). We use the method of similar ratios to find a relationship between the height and radius, h-y and x.

### What is the maximum possible volume of a cylinder?

Therefore the volume is a maximum when 2r−2h+h=0, so h=2r and hr=2. Show activity on this post. Show activity on this post. Let the ratio of height to radius be ρ, then h=ρr.

#### What is the maximum possible volume of a rectangular box that can be inscribed in the unit sphere?

Hence, the maximal volume of a rectangular box inside the sphere is 8r3/3√3.

How do I find the dimensions of a right circular cylinder of greatest volume that can be inscribed in a given right circular cone?

So our answer is: x= 23r 2 3 r . So the dimension of the right circular cylinder with the largest volume that can be inscribed in a right circular cone of radius r and altitude h is: The radius is two thirds of r.

What is the volume of the cylinder?

π r2 h
Solution: We know the volume of a cylinder is given by the formula – π r2 h, where r is the radius of the cylinder and h is the height.

## How do you find the maximum value of volume?

You can find the maximum of the volume by first finding the critical points of this function by finding the first derivative, then evaluating the second derivative at the critical points. If the second derivative is negative, that critical point is a maximum.

### How do you maximize a cylinder?

1. Set-Up (find the function to optimize) For a cylinder the volume is V=πr2h.
2. And for a cylinder with no top, the surface area is A=πr2+2πrh.
3. Given the area is 3π , we can express the volume using one variable instead of two. A=πr2+2πrh=3π .

#### What is the relation between sphere and cylinder?

(Answer: The sphere takes up two-thirds of the volume of the cylinder.)

What is the maximum possible volume of a right circular cone inscribed in a sphere of radius r?

The volume of the largest right circular cone that can be inscribed in a sphere of the radius R is (32/81)πR3 cubic units or (8/27) times the volume of the sphere.

What is volume of the sphere?

The formula for the volume of a sphere is V = 4/3 πr³. See the formula used in an example where we are given the diameter of the sphere.

## What is the formula of cylindrical?

V=πr2h
The formula for the volume of a cylinder is V=Bh or V=πr2h . The radius of the cylinder is 8 cm and the height is 15 cm. Substitute 8 for r and 15 for h in the formula V=πr2h . Simplify.

### How do you find the maximum and minimum volume?

To find the maximum possible volume, add the greatest possible error to each measurement, then multiply. To find the minimum possible volume, subtract the greatest possible error from each measurement, then multiply.

#### How do you find the maximum volume of a gas?

Calculating the volume of a gas

1. Volume = amount in mol × molar volume.
2. Volume = 0.25 × 24.
3. = 6 dm 3