Answer:
![r=\sqrt{\frac{3V}{\pi\ h}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%5Cfrac%7B3V%7D%7B%5Cpi%5C%20h%7D%7D)
Step-by-step explanation:
The volume of cone is given by:
![V=\frac{1}{3}\pi\ r^2\ h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5C%20r%5E2%5C%20h)
where
is the radius of the base and
is the height of the cone.
We need to solve for ![r](https://tex.z-dn.net/?f=r)
we have ![V=\frac{1}{3}\ \pi\ r^2\ h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5C%20%5Cpi%5C%20r%5E2%5C%20h)
Multiplying both sides by 3 to remove ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
⇒ ![3\times V=3\times \frac{1}{3}\ \pi\ r^2\ h](https://tex.z-dn.net/?f=3%5Ctimes%20V%3D3%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%5C%20%5Cpi%5C%20r%5E2%5C%20h)
⇒ ![3V=\pi\ r^2\ h](https://tex.z-dn.net/?f=3V%3D%5Cpi%5C%20r%5E2%5C%20h)
dividing both sides by ![\pi\ h](https://tex.z-dn.net/?f=%5Cpi%5C%20h)
⇒ ![\frac{3V}{\pi\ h}=\frac{\pi r^2 h}{\pi\ h}](https://tex.z-dn.net/?f=%5Cfrac%7B3V%7D%7B%5Cpi%5C%20h%7D%3D%5Cfrac%7B%5Cpi%20r%5E2%20h%7D%7B%5Cpi%5C%20h%7D)
⇒ ![\frac{3V}{\pi\ h}=r^2](https://tex.z-dn.net/?f=%5Cfrac%7B3V%7D%7B%5Cpi%5C%20h%7D%3Dr%5E2)
Taking square root both sides:
⇒ ![\sqrt{\frac{3V}{\pi\ h}}=\sqrt{r^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B3V%7D%7B%5Cpi%5C%20h%7D%7D%3D%5Csqrt%7Br%5E2%7D)
⇒ ![\sqrt{\frac{3V}{\pi\ h}}=r](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B3V%7D%7B%5Cpi%5C%20h%7D%7D%3Dr)
∴ ![r=\sqrt{\frac{3V}{\pi\ h}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%5Cfrac%7B3V%7D%7B%5Cpi%5C%20h%7D%7D)
Answer:
x=55°
Step-by-step explanation:
x=90-35
x=55°
(because its x+35=90°)
<u>The answer is 808/99</u>
Answer:
![x = \frac{25}{9}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B25%7D%7B9%7D)
Step-by-step explanation:
Divide both sides by 9 to isolate x:
![\frac{9x}{9} = \frac{25}{9} \\x = \frac{25}{9}\\](https://tex.z-dn.net/?f=%5Cfrac%7B9x%7D%7B9%7D%20%3D%20%5Cfrac%7B25%7D%7B9%7D%20%20%5C%5Cx%20%3D%20%5Cfrac%7B25%7D%7B9%7D%5C%5C)
Hope this helps!