I am eating ice cream in a cone. The cone radius is .5 inches and the cone height is 4 inches. If i packed it 2/3rds the way with ice cream, how much volume in ice cream is there?
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In this problem, we have an ice cream cone with a radius of 0.5 inches and a height of 4 inches. The ice cream fills two-thirds of the cone. We need to find the volume of the ice cream. To solve this, we'll first calculate the total volume of the cone, then find two-thirds of that volume.
To find the volume of ice cream, we first need to calculate the total volume of the cone. The formula for the volume of a cone is one-third times pi times radius squared times height. Substituting our values, we get one-third times pi times 0.5 inches squared times 4 inches. This simplifies to one-third times pi times 0.25 square inches times 4 inches, which equals one-third times pi times 1 cubic inch. So the total volume of the cone is pi over 3 cubic inches.
Now that we know the total volume of the cone is pi over 3 cubic inches, we can calculate the volume of the ice cream. Since the ice cream fills two-thirds of the cone, we multiply the total volume by two-thirds. So, the volume of ice cream equals two-thirds times pi over 3 cubic inches, which simplifies to two pi over nine cubic inches. Using the value of pi as approximately 3.14159, this gives us about 0.698 cubic inches of ice cream.
Let's summarize the solution to this ice cream cone problem. First, we calculated the volume of the full cone using the formula one-third times pi times radius squared times height. With a radius of 0.5 inches and a height of 4 inches, we found that the total volume of the cone is pi over 3 cubic inches. Next, since the ice cream fills two-thirds of the cone, we multiplied the total volume by two-thirds to get two pi over nine cubic inches. This equals approximately 0.698 cubic inches of ice cream. We solved this problem by applying the formula for the volume of a cone and using the given proportion of ice cream.