# A cylinder container 18 inches tall and a diameter of 12 inches is completely filled with vanilla, chocolate, and strawberry ice cream in a ratio of 32:1. What is the volume of strawberry ice cream in the container?

There are 339.3 cubic inches of strawberry ice cream.

Assuming you mean vanilla:chocolate:strawberry in a 3:2:1 ratio, here's what you do:

Think of the ratio as meaning "3 parts vanilla" to "2 parts chocolate" to "1 part strawberry".

That means there are six "parts" in total, and one is strawberry. So, the strawberry takes up one-sixth of the volume.

You could calculate the entire volume of the cylinder and take one-sixth of that amount, but it's quicker to take one-sixth of the height (3 inches) and find the volume of a cylinder 3 inches high and 12 inches in diameter.

To find volume of a cylinder, calculate the area of the base (a circle with a radius of 6 inches) and multiply by the height.

Area = #pir^2=pi6^2 = 113.1 square inches

Now multiply by the height of 3 inches, and you get 339.3 cubic inches of strawberry ice cream.

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First, calculate the volume of the entire cylinder using the formula for the volume of a cylinder:

[ V_{\text{cylinder}} = \pi r^2 h ]

Given that the diameter is 12 inches, the radius (r) is half of that, which is ( \frac{12}{2} = 6 ) inches. The height (h) is given as 18 inches.

[ V_{\text{cylinder}} = \pi (6^2)(18) ]

[ V_{\text{cylinder}} = 648\pi ]

Now, to find the volume of the strawberry ice cream, we need to calculate the ratio of strawberry ice cream to the total ice cream.

The ratio of strawberry ice cream to the total ice cream is given as 32:1. This means out of every ( 32 + 1 = 33 ) parts, 1 part is strawberry ice cream.

So, the fraction of the cylinder that is filled with strawberry ice cream is ( \frac{1}{33} ) of the total volume.

[ V_{\text{strawberry}} = \frac{1}{33} \times 648\pi ]

[ V_{\text{strawberry}} = \frac{648\pi}{33} ]

[ V_{\text{strawberry}} \approx 19.63 , \text{in}^3 ]

Therefore, the volume of strawberry ice cream in the container is approximately 19.63 cubic inches.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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