Answer: 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 :
[tex]V=\dfrac{4}{3}\pi r^3[/tex], where r is the radius of sphere.
[tex]\Rightarrow\ V=\dfrac{4}{3}x^3[/tex]
The volume of cone is given by :
[tex]V=\dfrac{1}{3}\pi r^2\ h[/tex], where r is the radius and h is height of the cone .
[tex]\Rightarrow\ V=\dfrac{1}{3}\pi (\dfrac{x}{2})^2(\dfrac{x}{2})\\\\\Rightarrow\ V=\dfrac{1}{24}x^3[/tex]
The number of cones would it take to equal the volume of the sphere is given by :-
[tex]n=\dfrac{\text{Volume of sphere}}{\text{Volume of cone}}\\\\=\dfrac{\dfrac{4}{3}x^3}{\dfrac{1}{24}x^3}=32[/tex]
