Question

A cone’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 

Answer 1

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 :

$V=\dfrac{4}{3}\pi r^3$, where r is the radius of sphere.

$\Rightarrow\ V=\dfrac{4}{3}x^3$

The volume of cone is given by :

$V=\dfrac{1}{3}\pi r^2\ h$, where r is the radius and h is height  of the cone .

$\Rightarrow\ V=\dfrac{1}{3}\pi (\dfrac{x}{2})^2(\dfrac{x}{2})\\\\\Rightarrow\ V=\dfrac{1}{24}x^3$

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

$n=\dfrac{\text{Volume of sphere}}{\text{Volume of cone}}\\\\=\dfrac{\dfrac{4}{3}x^3}{\dfrac{1}{24}x^3}=32$

Answer 2

Answer:

C) 32

Step-by-step explanation: