A waffle cone has a width of 7.6 cm and height of 15.2cm and a chocolate coating that is 2mm thick. What is the volume of the chocolate coating? How many of these cones if they were filled up to the brim would be needed for 400 gallons of ice cream given 2 gallons is 0.01m^3?

What i already know:
V of the cone without chocolate coating:229.84m^3
V of the cone with chocolate coating:258.03m^3
V of the chocolate coating:32.53m^3

PLEASE HELP ME - NOT ONLY AM I CONFUSED BUT I ALSO WANT TO HIT THE PROBLEM ALREADY.

Thanks to anyone who will help :)
XOXO, CJ

it looks like you just added .2 cm to the height and .2 cm to (1/2) the width, then used the formula for volume of the cone.

For all practical purposes, this will be ok.
But, ...
There is a rather complicated calcululation needed for the extensions at the vertex of the cone and the base of the cone
Draw a cross-section of the cone with r= 3.8 and h = 15.2
Now draw a larger cross-section around it so that the distance between the two triangles is .2 cm
From the top of the original triangle draw a perpendicular to the new side and extend the height to meet the new triangle.
The extension of the height will be hypotenuse of a small right-angled triangle, where you know one of the sides to be .2
You will need the angle at the top.
That angle will be equal to the angle formed by the original height and the side of the original cone.
let that angle be Ø
tanØ = 3.8/15.2 = ....
you can find Ø

now in the little triangle, let the hypotenuse be h
sinØ = 0.2/h
h = 0.2/sinØ

Of course at the base we can just add 0.2 to the origianal height.
So new height = 15.2 + h + 0.2

you will have to do a similar calculation at the base of the cone.
remember that the angle there will be 90-Ø

Good luck.

BTW, the answers you gave should have been in cm^3 , not m^3

For you second part, you are only concerned with the volume of the original cone, the chocolate cover does not affect how much the cone can hold.

To find the volume of the chocolate coating, let's first calculate the volume of the waffle cone:

Volume of waffle cone = (1/3) * base area * height

The base area of the cone can be calculated using the formula for the area of a circle:

Base area = π * (radius^2)

Given the width of the cone (diameter) is 7.6 cm, the radius would be half of that:

Radius = 7.6 cm / 2 = 3.8 cm

Converting the radius to meters:

Radius = 3.8 cm * 0.01 m/cm = 0.038 m

Now we can calculate the base area:

Base area = π * (0.038 m)^2

Next, we need to find the height of the cone. Given the height is 15.2 cm, we convert it to meters:

Height = 15.2 cm * 0.01 m/cm = 0.152 m

Now we can calculate the volume of the waffle cone:

Volume of waffle cone = (1/3) * π * (0.038 m)^2 * 0.152 m

Simplifying the equation:

Volume of waffle cone = 0.000742 m^3

Now, the volume of the waffle cone with the chocolate coating:

Volume of cone with chocolate coating = Volume of waffle cone + Volume of chocolate coating

You mentioned that the volume of the cone without the coating is 229.84 m^3, so we can substitute this value into the equation:

Volume of cone with chocolate coating = 229.84 m^3 + Volume of chocolate coating

Solving for the volume of the chocolate coating:

Volume of chocolate coating = Volume of cone with chocolate coating - Volume of waffle cone

Now you can substitute the given values into the equation to find the volume of the chocolate coating, which you already have calculated: 32.53 m^3.

For the second part of your question, we need to convert gallons to cubic meters:

2 gallons = 0.01 m^3

So if 2 gallons is equal to 0.01 m^3, we can find how many cones are needed for 400 gallons (V) by multiplying:

Number of cones = V / 0.01

Substitute the given value of 400 gallons:

Number of cones = 400 gallons / 0.01

Convert gallons to cubic meters:

Number of cones = 400 gallons * 0.01 m^3/gallon

Simplifying the equation:

Number of cones = 4,000 cones

Therefore, you would need 4,000 of these cones if they were filled up to the brim to store 400 gallons of ice cream.