I have 2 inches cubed of ice cream. I also have an ice cream cone with a radius of 1 inch and a height of 6 inches. If I packed the ice cream into the cone, what fraction of the cones volume would I fill up?
视频信息
答案文本
视频字幕
We have an ice cream problem to solve. We're given 2 cubic inches of ice cream and a cone with radius 1 inch and height 6 inches. We need to find what fraction of the cone's volume the ice cream would fill.
To solve this problem, we first need to calculate the 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: radius equals 1 inch and height equals 6 inches, we get one-third times pi times 1 squared times 6, which simplifies to 2 pi cubic inches.
Now we can calculate the fraction of the cone that would be filled. The fraction equals the volume of ice cream divided by the volume of the cone. This gives us 2 divided by 2 pi, which simplifies to 1 over pi. Therefore, the ice cream would fill one over pi of the cone's volume.
To summarize our solution: We had 2 cubic inches of ice cream and a cone with volume 2 pi cubic inches. The fraction of the cone filled is 2 divided by 2 pi, which equals 1 over pi. Therefore, the ice cream would fill exactly 1 over pi of the cone's total volume.