# Show that the volume of greatest culinder that can be inscribed in a cone of height h and semi vertical angle alpha is 4/27 pi h cube tan square alpha

Dear Student!

Let VAB be a given cone of height h, semi-vertical angle α and let x be the radius of the base of the cylinder A´ B´ DC. Which is inscribed in the cone VAB.

Then,

OO´ = height of the cylinder

⇒ OO´ = VO – VO´ = hx cot α

Let V be the volume of the cylinder. Then

V = πx2 (hx cot α)  ...... (1)

for maximum of minimum V we must have

Hence V is maximum when

The maximum volume of the cylinder is given by

Cheers!

• 54

in all maxima and minima word problems u haev to represent the equation in one variable like in this question,the hieght and the radius of the cylinder are the variables and since the height of the cylinder is given threfore represent the radius of the cylinder in terms of h and find the maxima or minima

• -1

Actually ur qn is a NCERT qn. So u can get de answer frm meritnation itself.

• 6

Thank you my friend! I already know that! Since i didnt understand the method i just asked this question to get the clarification

• -8

Thank you my friend

• -3
What are you looking for?