Question

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

Answer 1

The answer is 15 in³.

The volume of the cone is:
$V_1= \pi r_1 ^{2} \frac{h_1}{3} = \frac{ \pi r_1^{2} h_1}{3}$
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:
$V_1= \frac{ \pi r^{2} h}{3}$
$V_2= \pi rh^{2}$

We can include V₂ into V₁:
$V_1= \frac{V_2}{3}$

⇒ $V_2=3*V_1$
$V_2=3*5 in^{3}$
$V_2=15 in^{3}$