Question

Solve the equation for the bold variable (h).

Answer 1

In order to solve for the bold variable, we follow the order of operations. In this case h = S/(2(pi)r) - r

S = 2(pi)r^2 + 2(pi)rh ----> Subtract 2(pi)r^2 from both sides

S - 2(pi)r^2 = 2(pi)rh ----> Divide by 2(pi)r

S/(2(pi)r) - r = h

Answer 2

The solution for h is h = -r + s/(2πr).

The equation is 2πr^2 + 2πrh = s

After solving the equation for h, we get:

h = -r + s/(2π*r)

Here is the step-by-step solution:

Move all terms with h to one side:

2πr^2 = -2πr*h + s

Factor out h:

2πr*(-h) = -2πr^2 + s

Divide both sides by -2πr:

h = (-2πr^2 + s) / (-2πr)

Simplify:

h = r - s/(2πr)

Therefore, h = -r + s/(2πr)