Question

a right circural come is circumscribed over a sphere with radius of 10”. find the dimensions of the smallest such cone

Answer 1

Here, the right circular cone is circumscribed over a sphere with radious of 10".

Applying Pythagorus theorem we get, 10/(h-10) =

i.e.,

i.e.,

Now, volume of the cone is : V =

i.e., V =

Now,

i.e.,

i.e.,

i.e., h(h-40) = 0

i.e., h = 0, 40

Here h is greater then the radious of the sphere. Then, h can't be 0.

Therefore, h = 40.

And,

i.e.,

i.e.,

Hence, the height and radious of base are 40" and .