How do you find the maximum volume of a cylinder inscribed in a sphere?

Let R be the radius of the sphere and let h be the height of the cylinder centered on the center of the sphere. By the Pythagorean theorem, the radius of the cylinder is given by r2=R2−(h2)2. The volume of the cylinder is hence V=πr2h=π(hR2−h34).

What is the maximum volume of cone inscribed in a sphere?

Summary: 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 the height of the cylinder of maximum volume?

Solution: 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.

How do you maximize the volume of a cylinder?

The maximum volume occurs when r=1 ft and h=1 ft .

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 ratio of volume of cone inscribed in a sphere and the sphere?

Answer is (B) 4/3 See Fig.

What value of theta will maximize the troughs volume?

π/6
Thus, the maximum volume occurs when θ = π/6.

What is height of cylinder where volume is maximum when subscribed inside a hollow sphere of radius r is?

2R√3
Show that the height of the cylinder of maximum volume, that can be inscribed in a sphere of radius R is 2R√3.

What will be the maximum volume of the cylinder in cm3?

Also the knowledge of Pythagoras theorem is required. As it is clear from the figure below that the radius of the sphere = r cm, radius of the cylinder =R cm and the height of the cylinder = h cm. Hence, the volume of the largest cylinder that can be inscribed in a sphere of radius $3\sqrt 3 $ cm is $108 cm^3$.

How is the cylinder related to the sphere?

What is the relationship between the volume of the sphere and the volume of the cylinder? (Answer: The sphere takes up two-thirds of the volume of the cylinder.)