Surface Area Math Example 2

Solution

1. 1
   A cylinder has two circular bases (each area $\pi r^2$) and a curved lateral surface. If unrolled, the lateral surface is a rectangle with width $2\pi r$ (the circumference) and height $h$. Total: $SA = 2\pi r^2 + 2\pi r h$.
2. 2
   Substitute $r = 4$ cm and $h = 7$ cm: $SA = 2\pi(4)^2 + 2\pi(4)(7) = 2\pi(16) + 2\pi(28) = 32\pi + 56\pi$.
3. 3
   Combine: $SA = 88\pi$ cm² $\approx 276.5$ cm². Factor to check: $SA = 2\pi r(r + h) = 2\pi(4)(4 + 7) = 8\pi(11) = 88\pi$ ✓.