Question

Assume that you have an isosceles right triangle, with legs equal to 6 units, that is rotated around on one of its legs to generate a right circular cone. Find the volume of this cone.

Answer 1

First we need to see what is a right isosceles triangle is-
An Right triangle is one with one angle as , an Isosceles Tiangle means it has two sides of equal length, i.e. two angles are aslo equal so the Right Isosceles Triangle becomes the triangle with two sides of equal length and angle beween them as and the angle joining the hypotenues is each.

So now the leg of triangle is given as units, when it is roatated around on one of its legs to generate a right circular cone, it forms lik this-

So this cone will have height
And the base radius as , you can see that in above figure

So the volume of a Right Circular Cone-
Is given by-

Where is the base radius (leg around which it is rotated)
And is the perpedicular height of cone as triangle was isosceles right triangle (other equal leg of triangle)

So in terms of answer is volume units³
If we place we get volume units³

So volume of cone is-
units³
units³

^{(depends u write the answer in terms of or exact value)}