Answer:
*The height is 6 units.
*The radius is 8 units.
*The volume is exactly
cubic units.
An approximation for the volume would be
cubic units.
Step-by-step explanation:
To find the radius, we will have to use Pythagorean Theorem (or remember some Pythagorean Triples-either way).
Slant height=10 units (this is the hypotenuse length)
Radius=r units (trying to find this leg length)
Height=6 units (we are given this leg length)
So we have to solve:
![r^2+6^2=10^2](https://tex.z-dn.net/?f=r%5E2%2B6%5E2%3D10%5E2)
![r^2+36=100](https://tex.z-dn.net/?f=r%5E2%2B36%3D100)
Subtract 36 on both sides:
![r^2=64](https://tex.z-dn.net/?f=r%5E2%3D64)
Square root both sides:
![r=\sqrt{64}=8](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B64%7D%3D8)
The radius is 8 units.
To find the volume of a cone, we will use the formula
.
![V=\frac{1}{3} \pi (8)^2 (6)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%288%29%5E2%20%286%29)
![V=\frac{1}{3} \pi (64) (6)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%2864%29%20%286%29)
![V=\frac{1}{3}(64)(6) \pi](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%2864%29%286%29%20%5Cpi)
![V=128 \pi](https://tex.z-dn.net/?f=V%3D128%20%5Cpi%20)
So the volume is exactly
units cubed.
An approximation for this volume would be 402.124 units cubed (if we took an approximation of pi and multiply it to 128).