# How do you find the maximum volume of a cylinder inside a cone?

## How do you find the maximum volume of a cylinder inside a cone?

In this problem, first derive an equation for volume using similar triangles in terms of the height and radius of the cone. Once we have the modified the volume equation, we’ll take the derivative of the volume and solve for the largest value. The volume of the inscribed cylinder is V = πx^2(h-y).

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 volume of a cone that can be cut out from a sphere?

Thus the maximum volume of cone is 31×πr3cubic units when take out from solid hemisphere of radius r.

### What is the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a?

A sphere of fixed radius (R) is given. Let r and h be the radius and the height of the cylinder respectively. Hence, the volume of the cylinder is the maximum when the height of the cylinder is 2 R / √ 3.

What is the formula of a cylinder and a cone?

For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h.

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.

## What is the volume of the largest cone that can be inscribed in a hemisphere of radius of 7 cm?

Height of cone will also be 7 cm. Hence, required volume of largest cone is 359.34 cm³.

What is the volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm?

Answer: The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm^3.

What is height of cylinder?

height of a cylinder = V/ πr2. = 251.33 / 3.14 × 42.

### What is the maximum volume of right circular cone?

It is the value for which the volume is maximum. Hence maximum volume of cone is $2\sqrt{3}\pi$ cubic units.

What is volume of cylinder and cone?

The volume formulas for cones and cylinders are very similar: The volume of a cylinder is: π × r2 × h. The volume of a cone is: 1 3 π × r2 × h.

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

## How do you find the capacity of a cylinder?

Volume of a cylinder

1. V = A h.
2. Since the area of a circle = π r 2 , then the formula for the volume of a cylinder is:
3. V = π r 2 h.

What is the maximum volume of cone which is inscribed in a cylinder where radius of cylinder is 4cm and height is 7cm?