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**frustum**. Given here is a frustum of height h, top-radius r & base-radius R, which inscribes a right circular cylinder which in turn inscribes a sphere . The task is to find the largest possible volume of this sphere.

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## Optimization: Find Cylinder With Largest Volume Inscribed in a Sphere

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## How to find the volume of a cylinder inscribed in sphere?

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1.) Find the equation for the volume of a cylinder inscribed in a sphere. 2.) Find the derivative of the volume equation. 3.) Set the derivative equal to zero and solve to identify the critical points. 4.) Plug the critical points into the volume equation to find the maximum volume.

**π R 2 h**.

What is the radius of the cylinder inscribed in the sphere?

A cylinder is inscribed in a sphere with a radius of 20cm. Find the height, radius, and volume of the largest possible such cylinder. Radius of cylinder is R, radius of sphere is r, height is h, and volume is V.

What is the volume of the sphere to the cylinder?

Today, we are blessed with the understanding Calculus, and formulas for the volumes of basic shapes are taught to all in High School. What pleased Archimedes so much about the solution is that the ratio of the volume of the sphere to the cylinder is the same as the ratio of the surface area of the sphere to the surface area of the cylinder!

How to find the volume of a cylinder?

How to Calculate the Volume of a Cylinder. 1. Measure the circular base to get the diameter. 2. Divide the diameter by 2 to get the radius. 3. Calculate the area with the formula: A = πr^2, where r is the radius. 4. Measure the height of the cylinder. 5. Multiply the area by the height to get the …

How do you find the radius of a 20 cm sphere?

You know the formula for the volume of a cylinder: V = π r 2 h. You can express the radius of the cylinder r in terms of its hight h and one known quantity which in this case is the radius of the sphere that’s equal to 20 cm: r 2 = 20 2 − ( h 2) 2. Substitute r 2 in the formula with this expression and you get the following: V = π h ( 400 − h 2 4).

## What is a right circular cylinder?

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A right circular cylinder is inscribed in a sphere of radius r. Find the dimensions of such a – Brainly.com A right circular cylinder is inscribed in a sphere of radius r. Find the dimensions of such a cylinder with the largest possible volume (your answer may depend on r).

What is a right cylinder?

It is also called a right cylinder. All the points lying on the closed circular surface is at a fixed distance from a straight line known as the axis of the cylinder. The two circular bases of the right cylinder have the same radius and are parallel to each other.

What are the two circular bases of a right circular cylinder?

The two circular bases of the right circular cylinder have the same radius and are parallel to each other. It is one such geometric shape that is used frequently in real life. Basically, to derive the formulas for the surface area and volume of the cylinder, the right cylinder is considered.

What is the volume of a right circular cylinder?

Hence, the volume of the given right cylinder is 510.25 cubic m. TSA = 2 x 3.14 x 5 x 11.5 TSA = 361.1 sq.m Hence, the total surface area of the given right cylinder is 361.1 m 2. If the radius of circular bases and height of the right circular cylinder is given, then find the surface areas and volumes. What do you mean by right circular cylinder?

How to cut a right circular cylinder by a plane?

The section obtained on cutting a right circular cylinder by a plane, which contains two elements and parallels to the axis of the cylinder is the rectangle. When we revolve a rectangle about one side as the axis of revolution, a right cylinder is formed. Base: Each of the circular ends of a right circular cylinder is called its base.

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

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The cylinder itself is just the black part, the sphere is the red. I drew the height of the cylinder in green, the radius of the cylinder in purple, and the radius of the sphere (which you gave as 6 in) in orange.

**difference**between cylinder and sphere is that cylinder is (geometry) a surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve while sphere is (mathematics) a regular three-dimensional object in which every cross-section is a circle; the figure described by the revolution of a circle about its diameter.

What is a sphere in geometry?

A sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball a solid geometrical figure with straight parallel sides and a circular or oval cross section.

What is the difference between a cone and a cylinder?

A cone has a point and a varying circular cross-section around the axis between the point and the centre of the base. A cylinder has a constant circular cross-section around the axis between the centres of its ends.

What is the difference between spherical lenses and cylindrical lenses?

In many cases, one can have either of the two and astigmatism as well. Spherical lenses are lenses taken out from a sphere such as a ball. Where as, cylindrical lenses are lenses taken out from a surface of a cylinder like a tumbler. Cylindrical lenses have an axis associated with them.

What is the difference between a sphere and a cube?

A sphere has circular cross-sections however sliced, and all such cross-sections that pass through the centre of the sphere are identical. A cube has no circular cross-sections but six square faces (necessarily, three mutually perpendicular pairs of parallel faces).

## What is the height and radius of the cylinder inscribed inside?

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We know, the height and radius of the cylinder inscribed within the frustum is equal to the height and top-radius of the frustum respectively (Please refer here).So the height of the cylinder = h, radius of the cylinder = r.

**h**, radius of the cylinder = r. Also, radius of the sphere inscribed within a cylinder is equal to radius of the cylinder (Please refer here), so x = r.

References:

calculus – right circular cylinder inscribed in a sphere

A right cylinder is inscribed in a sphere of radius r. How …

A right circular cylinder is inscribed in a sphere of radius …

Largest sphere that can be inscribed in a right circular …

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What is a right cylinder?

What are the two circular bases of a right circular cylinder?

What is the volume of a right circular cylinder?

How to cut a right circular cylinder by a plane?

What is a right circular cylinder?

What is the height and radius of the cylinder inscribed inside?

What is a sphere in geometry?

What is the difference between a cone and a cylinder?

What is the difference between spherical lenses and cylindrical lenses?

What is the difference between a sphere and a cube?

What is the difference between the cylinder and the sphere?

What is the radius of the cylinder inscribed in the sphere?

What is the volume of the sphere to the cylinder?

How to find the volume of a cylinder?

How do you find the radius of a 20 cm sphere?

How to find the volume of a cylinder inscribed in sphere?

a right circular cylinder is inscribed in a sphere

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