Answer:
l = √109 in.
Explanation:
We see that the 10. in. apothem connecting the top of the cone and the circular base and a radius of the circle creates a right triangle.
Step 1: First we need to find the radius of the circle.
Since 6 is the diameter of the circle and the diameter is 2 * the radius, the radius is 3 in. since 2 * 3 = 6 and 6/2 = 3.
Step 2: Because we're working with a right triangle, we can now find l using the Pythagorean theorem, which is
a^2 + b^2 = c^2, where
- a and b are the shorter sides called legs,
- and c is the longest side called the hypotenuse.
We can plug in 10 for and 3 for b, allowing us to solve for c (aka l since l is the hypotenuse in the right triangle).
10^2 + 3^2 = c^2
100 + 9 = c^2
√109 = c
Thus, the measure of l is √109 in.