The ratio of total surface area to lateral surface area of a cylinder whose radius is 20 cm and height 60 cm, is

### Concept & Ratio Simplification Instead of calculating the full numerical areas, simplify the ratio of their formulas first. Total Surface Area (TSA): $$2\pi r(h + r)$$ Lateral (Curved) Surface Area (LSA): $$2\pi rh$$ ### Step-by-Step Solution * **Given:** Radius ($r$) = 20 cm, Height ($h$) = 60 cm. * Write the ratio expression: $$\frac{TSA}{LSA} = \frac{2\pi r(h + r)}{2\pi rh}$$ * Cancel the common terms ($2\pi r$): $$\frac{TSA}{LSA} = \frac{h + r}{h}$$ * Substitute the given values for $h$ and $r$: $$\frac{TSA}{LSA} = \frac{60 + 20}{60}$$ $$\frac{TSA}{LSA} = \frac{80}{60}$$ * Simplify the fraction: $$\frac{80}{60} = \frac{4}{3}$$ * The ratio is 4 : 3. ### Exam Strategy & Shortcut Always reduce formulas algebraically before plugging in numbers. Recognizing that $\frac{TSA}{LSA} = 1 + \frac{r}{h}$ makes it an instant mental calculation: $1 + \frac{20}{60} = 1 + \frac{1}{3} = \frac{4}{3}$. ### Common Pitfall Wasting time computing $2 \times \pi \times 20 \times 80$ and $2 \times \pi \times 20 \times 60$, which opens up opportunities for arithmetic mistakes. ### Final Answer Therefore, the correct answer is **4 : 3**.