The question "how much space is inside a solid?" is actually asking about the volume of that solid.
The volume of a cone is given by
where h is the height of the cone, and r is its radius.
So, you only need to plug in the values:
The number of pieces per stack after 3 cuts represented by a power expression can be written as
- The number of equal pieces per cut = 3
- The number of cuts made = 3
<u>Using a power </u><u>expression</u><u> </u><u>:</u>
- The number of of equal pieces per cut is raised to a power which represents the number of cuts made
- Thus we have
- After 1 cut ;
- After 2 cuts ;
- After 3 cuts ;
Therefore, the Number of pieces present in stack after 3 cuts is
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Use trigonometry to find the angle between the segments 3 and 6.
∠XOB = arccos(3/6) = 60°
The measure of arc AB is double that angle, since the figure is symmetrical about the line containing the segment of length 3.
m(arc AB) = 2·60° = 120°