is the volume of this ice cream cone?

Question

I made a large ice cream cone of a composite shape of a cone and hemisphere. If the height of the cone is 10, and the diameter of both the cone and the hemisphere is 6.

What is the volume of this ice cream cone?

Answer 1

Cone: V = (1/3)πr²H

V = (1/3)π(3)²(10)

V = (1/3)π(90)

V = 30π

 

Hemisphere: V = (1/2)(4/3)πr³

V = (2/3)π(6)³

V = (2/3)π(216)

V = 144π

 

Total Volume = 30π + 144π = 174π

V ≈ 546.64 units³

 

Answer 2

Anytime you deal with a composite shape, you should break it down into it's parts, and then find the volume of each part.  Remember, the whole is just the sum of its parts.

 

The cone has a height of 10 and a diameter of 6.  This means it has a radius of 3.

The volume of any cone is (1/3)πr²h.  Therefore the volume of this cone would be (1/3)π(3)²(10) or 30π units³.

 

The hemisphere has a diameter of 6.  This means it also has a radius of 3.

The volume of any sphere is (4/3)πr³.  A hemisphere would be half that or (2/3)πr³.  Therefore the volume of this hemisphere is (4/3)π(3)³ or 36π units³.

 

The total volume would be 30π + 36π or 66π units³.  The decimal approximation is 207.35 units³.

Answer 3

Separate the problem into two parts: the cone and the hemisphere.

 

The volume of a cone is (1/3)πr²h.  Just plug in the radius (half of the diameter) and the height of the cone to determine the volume of the cone.

 

The volume of a sphere is (4/3)πr³, but you have a hemisphere, so it would be half of that, or (2/3)πr³.  Again, just plug in the radius (half of the diameter) to get the volume of the hemisphere.

 

Once you have the volume of the cone and the volume of the sphere, just add them together for the final answer.