Question

find the height of this cone using the pythagorean theorem. pythagorean theorem: $a^{2}+b^{2}=c^{2}$

Explanation:

Step1: Identify the values for Pythagorean Theorem

The slant - height $c = 9$ in and the radius $b = 6$ in. We want to find the height $a$.

Step2: Rearrange the Pythagorean Theorem

From $a^{2}+b^{2}=c^{2}$, we get $a^{2}=c^{2}-b^{2}$.

Step3: Substitute the values

$a^{2}=9^{2}-6^{2}=81 - 36=45$.

Answer:

$\sqrt{45}$ in