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

Answer:

4

Step-by-step explanation:

1. the volume of the cone is:

$V_c=\frac{1}{3}\pi hR^2,$

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

2. the volume of the sphere is:

$V_s=\frac{4}{3}\pi *R^3,$

where 'π' - 3.1415.

3. according to the condition:

$V_c=V_s; => \frac{1}{3}\pi *h*R^2=\frac{4}{3} \pi*R^3; => h=4*R.$

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