The volume of a cylinder with height h h and radius r r can be found using the formula V = ? r 2 h V=?r2h Find the volume of a c
ylinder is 785.4 ft 3 ft3 . If the height is twice the radius what is the radius of the cylinder
1 answer:
Answer:
5.000 ft
Step-by-step explanation:
The formula for the volume of a cylinder is
V = πr²h
Data:
V = 785.4 ft³
h = 2r
Calculations:
V = πr²h = πr²(2r) = 2πr³
Divide each side by 2π
Take the cube root of each side
![r = \sqrt[3]{\frac{V }{2\pi}}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7BV%20%7D%7B2%5Cpi%7D%7D)
![= \sqrt[3]{\frac{785.4 }{2\pi }}](https://tex.z-dn.net/?f=%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B785.4%20%7D%7B2%5Cpi%20%7D%7D)
![= \sqrt[3]{125.00}](https://tex.z-dn.net/?f=%3D%20%5Csqrt%5B3%5D%7B125.00%7D)
= 5.000 ft
The radius of the cylinder is 5.000 ft.
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