Question

5 a set production designer creates a right circular cylindrical pillar. the desi surface of the pillar and needs to find the height for a reinforcement rod. use ( a=(2pi r)h+pi r^{2} ), where ( r ) represents the radius, ( h ) represents the surface area of the pillar. what is a formula for ( h ) in terms of the other varia

a ( h=\frac{a - pi r^{2}}{2pi r} )
b ( h=\frac{a+pi r^{2}}{2pi r} )
c ( h=\frac{a}{3pi r^{2}} )
d ( h=\frac{a}{2pi r}-\frac{1}{2} )

Explanation:

Step1: Isolate the term with h

Given $A=(2\pi r)h+\pi r^{2}$, subtract $\pi r^{2}$ from both sides: $A - \pi r^{2}=(2\pi r)h$.

Step2: Solve for h

Divide both sides by $2\pi r$: $h=\frac{A - \pi r^{2}}{2\pi r}$.

Answer:

A. $h=\frac{A - \pi r^{2}}{2\pi r}$