Final answer:
To solve the equation L = 3πrh + 5πr² for the variable h, rearrange the equation and isolate h on one side. The equation can be solved as h = L/(3πr) - 5r/3.
Step-by-step explanation:
To solve the equation L = 3πrh + 5πr², we can rearrange it to isolate the variable we want to solve for. In this case, let's solve for the variable h.
Step 1: Distribute the πr² to both terms in the equation.
L = 3πrh + 5πr² becomes: L = 3πrh + 5πr²
Step 2: Subtract 5πr² from both sides of the equation.
L - 5πr² = 3πrh
Step 3: Divide both sides of the equation by 3πr.
L/(3πr) - 5πr²/(3πr) = 3πrh/(3πr)
This simplifies to: L/(3πr) - 5r/3 = h
So, the equation is solved for h as h = L/(3πr) - 5r/3