2015年11月9日 · The best place to start is by drawing a diagram. The picture below shows the cylinder inscribed in the sphere. Given the height, #h#, we can find the radius of the cylinder in terms of #r# using the Pythagorean Theorem. Note that #h# refers to …

2015年6月11日 · A right circular cylinder is inscribed in a sphere of radius a > 0. What is the height of the cylinder when its volume is maximal?

2016年4月26日 · We want to maximize the volume of the cylinder: $V = \pi r^2 h$. We need to use our constraint that it is inscribed in a sphere of radius $R = 6$. Try looking at the picture and writing a relationship between $r$ (radius of cylinder), $h$ (height of cylinder), and $R = 6$. See if you can continue from here!

2017年10月30日 · 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 $V$. I used Pythagorean's Theorem to get $R^2 + \dfrac{h^2}{4} = r^2$.

2024年12月16日 · Misc 14 Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 2𝑅/√3 . Also find the maximum volume.Given Radius of sphere = R Let h be the height & 𝒙 be the diameter of cylinder In ∆ 𝑨𝑩𝑪 Using Pythagoras theorem (𝐶𝐵)^2+(𝐴𝐵)^2=(𝐴𝐶

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

The surface area of a cylinder = 2πr 2 + 2πrh (or) 2πr(r + h), where r is the radius of the cylinder and h is the height of the cylinder. Calculations: Let R be the radius of the sphere and is a constant. Let a and h be the radius( is a variable) and height of the cylinder that can be inscribed in a sphere of radius R as shown in the below ...

2025年2月5日 · Given: A cylinder is inscribed in a sphere The radius of the sphere is \(\frac{5}{6}\) times the height of the cylinder. Formula used: Volume of c

2012年11月22日 · A right circular cylinder is inscribed in a sphere with radius R. Find the largest possible volume of such a cylinder. Solution: To visualize the problem, let's draw the figure first. Inscribed means inside and so a right circular cylinder is located inside the sphere.

Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to \[ \frac{2}{3} \] of the diameter of the sphere. Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface is \[\cot^{- 1} \left( \sqrt{2} \right)\] .