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?

Part 1)

Part 2)  

Part 3)

Part 4)

Step-by-step explanation:

Part 1) Find the volume of the cone

The volume of the cone is equal to

we have

----> the radius is half the diameter

substitute

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

The volume of a hemisphere is

we have

----> the radius is half the diameter of the base's cone

substitute

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

Part 4) Find the volume of the new cone

The volume of the cone is equal to

we have

substitute

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

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

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)

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step-by-step explanation:

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