Answer:
Therefore, the volume of the cone is V=4π.
Step-by-step explanation:
From task we have a circular cone with radius 2 m and height 3 m. We use the disk method to find the volume of this cone.
We have the formula:
We know that r=2 and h=3, and we get:
![V=\int_0^3\pi \cdot \left(\frac{2}{3}x\right)^2\, dx\\\\V=\int_0^3 \pi \frac{4}{9}x^2\, dx\\\\V= \frac{4\pi}{9} \int_0^3 x^2\, dx\\\\V= \frac{4\pi}{9} \left[\frac{x^3}{3}\right]_0^3\, dx\\\\V= \frac{4\pi}{9}\cdot 9\\\\V=4\pi](https://tex.z-dn.net/?f=V%3D%5Cint_0%5E3%5Cpi%20%5Ccdot%20%5Cleft%28%5Cfrac%7B2%7D%7B3%7Dx%5Cright%29%5E2%5C%2C%20dx%5C%5C%5C%5CV%3D%5Cint_0%5E3%20%5Cpi%20%5Cfrac%7B4%7D%7B9%7Dx%5E2%5C%2C%20dx%5C%5C%5C%5CV%3D%20%5Cfrac%7B4%5Cpi%7D%7B9%7D%20%5Cint_0%5E3%20x%5E2%5C%2C%20dx%5C%5C%5C%5CV%3D%20%5Cfrac%7B4%5Cpi%7D%7B9%7D%20%5Cleft%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%5Cright%5D_0%5E3%5C%2C%20dx%5C%5C%5C%5CV%3D%20%5Cfrac%7B4%5Cpi%7D%7B9%7D%5Ccdot%209%5C%5C%5C%5CV%3D4%5Cpi)
Therefore, the volume of the cone is V=4π.
You have to calculate how many combinations of 6 people can be chosen from 11. The formula for this is:
n! / [r! * (n-r)!]
combinations = 11! / [6! * 5!] =
11 * 10 * 9 * 8 * 7 / 5 * 4 * 3 * 2 *1 =
11 * 3 * 2 * 7 =
462 Combinations
Source:
http://www.1728.org/combinat.htm
It’s the third one!!! 1/2x-2
Answer:
Step-by-step explanation:
