Question

A right cone has a base with diameter 6 units. The volume of the cone is 72π cubic units.

What is the length of a segment drawn from the apex to the edge of the circular base?
Round to the nearest tenth. This is a multi-step problem.
The segment drawn from the apex to the edge of the circular base is _______ units.

Answer 1

6

Explanation:

The radius of the base of the cone is 3 units, since the diameter is 6 units. Let's call the height of the cone "h".

We can use the formula for the volume of a cone to find h:

V = (1/3)πr^2h

72π = (1/3)π(3^2)h

72π = (1/3)π(9)h

72π = 3πh

h = 72/3

h = 24

Now we can use the Pythagorean theorem to find the length of the segment:

a^2 + h^2 = c^2

a^2 + 24^2 = 6^2

a^2 = 36

a = 6

So the segment drawn from the apex to the edge of the circular base is 6 units, rounded to the nearest tenth.