Answer:
Volume: ![\frac{2}{3}\pi r^3](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%5Cpi%20r%5E3)
Ratio: ![\frac{2}{9}r](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B9%7Dr)
Step-by-step explanation:
First of all, we need to find the volume of the hemispherical tank.
The volume of a sphere is given by:
![V=\frac{4}{3}\pi r^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3)
where
r is the radius of the sphere
V is the volume
Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:
![V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3](https://tex.z-dn.net/?f=V%27%3D%5Cfrac%7BV%7D%7B2%7D%3D%5Cfrac%7B%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%7D%7B2%7D%3D%5Cfrac%7B2%7D%7B3%7D%5Cpi%20r%5E3)
Now we want to find the ratio between the volume of the hemisphere and its surface area.
The surface area of a sphere is
![A=4 \pi r^2](https://tex.z-dn.net/?f=A%3D4%20%5Cpi%20r%5E2)
For a hemisphere, the area of the curved part of the surface is therefore half of this value, so
. Moreover, we have to add the surface of the base, which is
. So the total surface area of the hemispherical tank is
![A'=2\pi r^2 + \pi r^2 = 3 \pi r^2](https://tex.z-dn.net/?f=A%27%3D2%5Cpi%20r%5E2%20%2B%20%5Cpi%20r%5E2%20%3D%203%20%5Cpi%20r%5E2)
Therefore, the ratio betwen the volume and the surface area of the hemisphere is
![\frac{V'}{A'}=\frac{\frac{2}{3}\pi r^3}{3\pi r^2}=\frac{2}{9}r](https://tex.z-dn.net/?f=%5Cfrac%7BV%27%7D%7BA%27%7D%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B3%7D%5Cpi%20r%5E3%7D%7B3%5Cpi%20r%5E2%7D%3D%5Cfrac%7B2%7D%7B9%7Dr)
Answer:
Step-by-step explanation:
Supplementary angles sum to 180 degrees.
x+118=180
x=62 degrees
Answer:
<h2><em><u>Option</u></em><em><u> </u></em><em><u>A</u></em><em><u> </u></em><em><u>and</u></em><em><u> </u></em><em><u>C</u></em></h2>
Step-by-step explanation:
As,
![2 \sqrt{75} + 3 \sqrt{50}](https://tex.z-dn.net/?f=2%20%5Csqrt%7B75%7D%20%20%2B%203%20%5Csqrt%7B50%7D%20)
![= 2 \sqrt{25 \times 3} + 3 \sqrt{25 \times 2} (A)](https://tex.z-dn.net/?f=%20%3D%202%20%5Csqrt%7B25%20%5Ctimes%203%7D%20%20%2B%203%20%5Csqrt%7B25%20%5Ctimes%202%7D%20%28A%29%20)
![= 2 \times 5 \sqrt{3} + 3 \times 5 \sqrt{2}](https://tex.z-dn.net/?f=%20%3D%202%20%5Ctimes%205%20%5Csqrt%7B3%7D%20%20%2B%203%20%5Ctimes%205%20%5Csqrt%7B2%7D%20)
![= 10 \sqrt{3} + 15 \sqrt{2} (C)](https://tex.z-dn.net/?f=%20%3D%2010%20%5Csqrt%7B3%7D%20%20%2B%2015%20%5Csqrt%7B2%7D%20%28C%29)
Answer:
adenosine triphosphate.
Step-by-step explanation: