Outer CSA Calculation

Calculate the curved surface area of the main cylinder with radius $r=5$ cm and height $h=7$ cm: $2 \pi r h = 2 \pi (5)(7) = 70 \pi$.

$2 \pi r h = 70 \pi$

Base and Ring Surface Area

The area of the bottom circular base is $\pi r^2 = 25 \pi$. The top surface is a ring with area $\pi r^2 - \pi r_h^2 = 25 \pi - 9 \pi = 16 \pi$.

$\text{Area} = 25 \pi + 16 \pi = 41 \pi$

Inner Hole Surface Area

The inner wall area (curved surface of the hole) with depth $d=2$ cm and radius $r_h=3$ cm is $2 \pi r_h d = 2 \pi (3)(2) = 12 \pi$.

$2 \pi r_h d = 12 \pi$

Total Surface Area

Summing all surfaces: $70 \pi + 41 \pi + 12 \pi = 132 \pi$ cm².

$70 \pi + 41 \pi + 12 \pi = 132 \pi$