Question

Suppose that the radius of the base of a cone is R. Suppose, moreover, that the volume

of the cone is the same as the volume of the sphere with radius R (same as the base radius of
the cone). How many times is the height of the cone larger than R?

Answer 1

4

Explanation:

1. the volume of the cone is:

`V_c=(1)/(3)\pi hR^2,`

where 'h' - the height of the cone, 'π' - 3.1415.

2. the volume of the sphere is:

`V_s=(4)/(3)\pi *R^3,`

where 'π' - 3.1415.

3. according to the condition:

`V_c=V_s; => (1)/(3)\pi *h*R^2=(4)/(3) \pi*R^3; => h=4*R.`

4. h=4R means 4 time the height of the cone is larger then R.