Cylinder – curved surface area from radius and height: Find the curved (lateral) surface area of a right circular cylinder with radius 7 cm and height 160 cm. Give the answer in cm^2.

Introduction / Context:The curved surface area (CSA) of a cylinder equals the area of a rectangle with height h and width equal to the circumference 2πr. This is a direct substitution exercise once r and h are identified correctly.

Given Data / Assumptions:

• r = 7 cm
• h = 160 cm
• CSA = 2πrh

Concept / Approach:Compute 2 * π * 7 * 160 and evaluate numerically, preferably with π = 22/7 to get an exact integer in this setup (common in aptitude problems).

Step-by-Step Solution:CSA = 2πrh = 2 * π * 7 * 160 = 2240π cm^2With π = 22/7 → CSA = 2240 * (22/7) = 320 * 22 = 7040 cm^2

Verification / Alternative check:Using π ≈ 3.14 yields 2240 * 3.14 ≈ 7033.6 cm^2, which rounds to 7034–7040; consistent with the exact 22/7 value.

Why Other Options Are Wrong:6020 and 5052 are too small; 7045 and 7080 overshoot the precise value; 7040 cm^2 matches the exact arithmetic with π = 22/7.

Common Pitfalls:Using diameter instead of radius; confusing TSA with CSA; arithmetic errors multiplying large factors.

Final Answer:7040 sq cm