C) 2:3 and 12:18
bcs you put them in fraction form and cross multiply them
Answer:
r = 5.848cm, h = 11.696cm
Step-by-step explanation:
Surface area: ![SA=2\pi rh+2\pi r^2](https://tex.z-dn.net/?f=SA%3D2%5Cpi%20rh%2B2%5Cpi%20r%5E2)
Volume: ![V=\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2h)
Therefore, the height of a cylinder given its volume would be
, thus:
![SA=2\pi r(\frac{V}{\pi r^2})+2\pi r^2\\\\SA=\frac{2V}{r}+2\pi r^2\\\\SA=\frac{2(400\pi)}{r}+2\pi r^2\\\\SA=\frac{800\pi}{r}+2\pi r^2](https://tex.z-dn.net/?f=SA%3D2%5Cpi%20r%28%5Cfrac%7BV%7D%7B%5Cpi%20r%5E2%7D%29%2B2%5Cpi%20r%5E2%5C%5C%5C%5CSA%3D%5Cfrac%7B2V%7D%7Br%7D%2B2%5Cpi%20r%5E2%5C%5C%5C%5CSA%3D%5Cfrac%7B2%28400%5Cpi%29%7D%7Br%7D%2B2%5Cpi%20r%5E2%5C%5C%5C%5CSA%3D%5Cfrac%7B800%5Cpi%7D%7Br%7D%2B2%5Cpi%20r%5E2)
We now find the derivative of the surface area of the cylinder with respect to its radius and set it equal to 0, solving for the radius:
![\frac{d(SA)}{dr}=-\frac{800\pi}{r^2}+4\pi r](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28SA%29%7D%7Bdr%7D%3D-%5Cfrac%7B800%5Cpi%7D%7Br%5E2%7D%2B4%5Cpi%20r)
![0=-\frac{800}{r^2}+4\pi r](https://tex.z-dn.net/?f=0%3D-%5Cfrac%7B800%7D%7Br%5E2%7D%2B4%5Cpi%20r)
![0=800\pi+4\pi r^3](https://tex.z-dn.net/?f=0%3D800%5Cpi%2B4%5Cpi%20r%5E3)
![-800\pi=4\pi r^3](https://tex.z-dn.net/?f=-800%5Cpi%3D4%5Cpi%20r%5E3)
![-200=r^3](https://tex.z-dn.net/?f=-200%3Dr%5E3)
![r\approx5.848](https://tex.z-dn.net/?f=r%5Capprox5.848)
If
, then the surface area of the cylinder increases
Therefore, the surface area is minimized when the radius is
, making the minimum height
.
In conclusion, the 2nd option is correct.
Answer: 4311/9900 = 0.4354 4936/990 = 4.985 530/900 = 0.58 674/990 = 0.680 8099/990 = 8.180 explanation: divide the numbers and select the answers.
Answer:
320
Step-by-step explanation:
4*80=320
Answer:
2 divided by 1/2 is 4.
Step-by-step explanation: