Question

A cone has a volume of 5 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?

15 in3
20 in3
25 in3
30 in3

Answer 1

The answer is 15 in³.

The volume of the cone is:

`V_1= \pi r_1 ^(2) (h_1)/(3) = ( \pi r_1^(2) h_1)/(3)`
where:
V₁ - the volume of the cone
r₁ - the radius of the cone
h₁ - the height of the cone

The volume of the cylinder is:

`V_2= \pi r_2h_2^(2)`
where:
V₂ - the volume of the cone
r₂ - the radius of the cone
h₂ - the height of the cone

Since the cone fits exactly inside of the cylinder, they have the same radius and the height:
r₁ = r₂
h₁ = h₂

Also:
V₁ = 5

Now, let's write two volume formulas together:

`V_1= ( \pi r^(2) h)/(3)`

`V_2= \pi rh^(2)`

We can include V₂ into V₁:

`V_1= (V_2)/(3)`

⇒
`V_2=3*V_1`

`V_2=3*5 in^(3)`

`V_2=15 in^(3)`