(0.064)(2*pi*h)+(0.064)*4*pi*r=z*2*pi*r*h
(0.064)2*pi*r=z*pi*r^2
pi*r^2*h=1567.8
Find r,h,z
To solve for the values of r, h, and z in the given equations, we can follow these steps:
1. Simplify the first equation:
(0.064)(2*pi*h) + (0.064)(4*pi*r) = z * (2*pi*r*h)
0.128*pi*h + 0.256*pi*r = 2*pi*r*h*z
2. Simplify the second equation:
(0.064)(2*pi*r) = z * (pi*r^2)
0.128*pi*r = pi*r^2*z
3. Simplify the third equation:
pi*r^2*h = 1567.8
Now, let's solve these equations step by step:
From the second equation, we can see that both sides have a factor of pi. We can divide both sides of the equation by pi:
0.128*r = r^2*z
Next, let's rearrange this equation to solve for z:
z = (0.128*r) / r^2
z = 0.128 / r
Now, substitute the value of z in the first equation:
0.128*pi*h + 0.256*pi*r = 2*pi*r*h*(0.128/r)
0.128*pi*h + 0.256*pi*r = 0.256*pi*r*h
Divide both sides of the equation by pi:
0.128*h + 0.256*r = 0.256*r*h
Now, let's rearrange this equation to solve for r:
0.256*r*h - 0.256*r = 0.128*h
r*(0.256*h - 0.256) = 0.128*h
r = 0.128*h / (0.256*h - 0.256)
Finally, let's substitute the values of r and z in the third equation:
pi*r^2*h = 1567.8
pi*(0.128*h / (0.256*h - 0.256))^2*h = 1567.8
Simplify this equation by expanding and rearranging:
pi*(0.016*h^2) / (0.064*h - 0.064)^2 = 1567.8
0.016*h^2 / (0.064*h - 0.064)^2 = 1567.8 / pi
h^2 / (0.004*h - 0.004)^2 = 1567.8 / (pi * 0.016)
Now, you can solve this equation using a numerical method or graphing calculator to find the value of h.
Once you have the value of h, substitute it back into the equation r = 0.128*h / (0.256*h - 0.256) to find the value of r.
Finally, substitute the values of r and h in the equation z = 0.128 / r to find the value of z.