A right cone has a base with diameter 10 units. The volume of the cone is 100𝜋 cubic units.
What is the length of a segment drawn from the apex to the edge of the circular base?
show your work
The formula for the volume of a cone is given by:
V = (1/3)πr^2h
Given that the diameter of the base is 10 units, the radius (r) of the base is half of the diameter, so r = 5 units.
And the volume of the cone is given as 100π cubic units, so:
100π = (1/3)π(5)^2h
100 = (1/3)(25)h
300 = 25h
h = 12
Now, we want to find the length of a segment drawn from the apex to the edge of the circular base, which forms a right triangle with height h and radius r.
Using the Pythagorean theorem, the length of the segment can be found as:
l = √(r^2 + h^2)
l = √(5^2 + 12^2)
l = √(25 + 144)
l = √169
l = 13
Therefore, the length of the segment drawn from the apex to the edge of the circular base is 13 units.