Question

1. You are opening a snow cone stand. Your cups, which are shaped like a cone, are 4" tall and have a 6" diameter. How much room is there in the cone without a top on the snow cone? (filled to the brim only)

2. The top of your snow cone is a perfect semicircle. It goes all the way across the cone. How many cubic inches of ice in the top of the snow cone?

3. How many cubic inches of snow cone will you be serving?

4.You want to start selling 2 different sizes of cones. You want your new cone to be twice as big as your current cone (top included). You found a cone that has a 6" diameter and is 8" tall. How many cubic inches of snow cone will you have with the new cone?

Answer 1

Part 1)
`12\pi\ in^(3)`

Part 2)
`18\pi\ in^(3)`

Part 3)
`30\pi\ in^(3)`

Part 4)
`42\pi\ in^(3)`

Explanation:

Part 1) Find the volume of the cone

The volume of the cone is equal to

`V=(1)/(3)\pi r^(2)h`

we have

`r=6/2=3\ in` ----> the radius is half the diameter

`h=4\ in`

substitute

`V=(1)/(3)\pi (3)^(2)(4)=12\pi\ in^(3)`

Part 2) Find the volume of a hemisphere (top of the snow cone)

The volume of a hemisphere is

`V=(4)/(6)\pi r^(3)`

we have

`r=6/2=3\ in` ----> the radius is half the diameter of the base's cone

substitute

`V=(4)/(6)\pi (3)^(3)=18\pi\ in^(3)`

Part 3) How many cubic inches of snow cone will you be serving?

Adds the volume of the cone and the volume of the top

`12\pi\ in^(3)+18\pi\ in^(3)=30\pi\ in^(3)`

Part 4) Find the volume of the new cone

The volume of the cone is equal to

`V=(1)/(3)\pi r^(2)h`

we have

`r=3\ in`

`h=8\ in`

substitute

`V=(1)/(3)\pi (3)^(2)(8)=24\pi\ in^(3)`

The volume of the top is the same, because the diameter of the cone is the same

`V=18\pi\ in^(3)`

Adds the volume of the new cone and the volume of the top

`24\pi\ in^(3)+18\pi\ in^(3)=42\pi\ in^(3)`