Question

1. the formula for the lateral area of a cylinder is a = 2πrh, where r is the radius and h is the height. solve the equation for h.

Explanation:

Step1: Identify the goal

We need to isolate \( h \) in the formula \( A = 2\pi rh \).

Step2: Divide both sides by \( 2\pi r \)

To solve for \( h \), we divide each side of the equation by \( 2\pi r \) (assuming \( 2\pi r
eq 0 \), which is valid since radius \( r \) of a cylinder is a positive real number).

$$ \frac{A}{2\pi r} = \frac{2\pi rh}{2\pi r} $$

Step3: Simplify the right side

The \( 2\pi r \) terms in the numerator and denominator on the right side cancel out, leaving us with:

$$ h = \frac{A}{2\pi r} $$

Answer:

\( h = \dfrac{A}{2\pi r} \)