Acone’s height and its radius are each equal to half the radius of a sphere. how many of these cones would it take to equal the volume of the sphere? a)16 b)24 c)32 d)48

  32

Step-by-step explanation:

Given: A cone’s height and its radius are each equal to half the radius of a sphere.

Let x be the radius of the sphere, then the radius of cone =x/2

and height of the cone = x/2

The volume of sphere is given by :

, where r is the radius of sphere.

The volume of cone is given by :

, where r is the radius and h is height  of the cone .

The number of cones would it take to equal the volume of the sphere is given by :-

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,