Cylinder – find radius from curved (lateral) surface area: A cylinder has lateral surface area (CSA) 94.2 cm^2 and height 5 cm. Using π = 3.14, compute the radius of its base.

Introduction / Context:The curved (lateral) surface area of a cylinder is the rectangle that wraps around: width equals the height h and length equals the circumference 2πr. This question checks algebraic manipulation of the CSA formula to recover r from given CSA and h.

Given Data / Assumptions:

• CSA = 94.2 cm^2
• Height h = 5 cm
• π = 3.14
• CSA formula: 2πrh

Concept / Approach:Rearrange 2πrh = CSA to r = CSA / (2πh). Substitute numeric values carefully and simplify.

Step-by-Step Solution:2πh = 2 * 3.14 * 5 = 31.4r = 94.2 / 31.4 = 3.0 cm

Verification / Alternative check:Plug back: 2πrh = 2 * 3.14 * 3 * 5 = 94.2 cm^2, matching exactly.

Why Other Options Are Wrong:5 cm and 4 cm make CSA too large; 8 cm is far too large; 2 cm would give only 62.8 cm^2, not 94.2 cm^2.

Common Pitfalls:Using πr^2h (volume) instead of 2πrh (CSA); multiplying by diameter in place of radius; rounding too early.

Final Answer:3 cm