The total surface area of a solid hemisphere of diameter 14 cm, is

### Concept & Total Surface Area of Hemisphere The total surface area of a solid hemisphere includes both its curved surface area and its flat circular base. $$TSA = 2\pi r^2 + \pi r^2 = 3\pi r^2$$ ### Step-by-Step Solution 1. **Given:** Diameter ($d$) = $14\text{ cm}$. 2. **Find Radius:** Radius ($r$) = $\frac{d}{2} = \frac{14}{2} = 7\text{ cm}$. 3. **Calculate Total Surface Area:** $TSA = 3\pi r^2$ $TSA = 3 \times \frac{22}{7} \times (7)^2$ $TSA = 3 \times \frac{22}{7} \times 49$ $TSA = 3 \times 22 \times 7$ $TSA = 66 \times 7 = 462\text{ cm}^2$ ### Exam Strategy & Shortcut When the radius is $7$, $14$, $21$, etc., use $\pi = \frac{22}{7}$ for quick cancellation. Memorizing that $\pi r^2$ for $r=7$ is $154$ allows you to jump straight to $3 \times 154 = 462$ instantly. ### Common Pitfall A common mistake is calculating only the curved surface area ($2\pi r^2 = 308\text{ cm}^2$) and forgetting to add the flat circular base area ($\pi r^2$) for a *solid* hemisphere. ### Final Answer Therefore, the correct answer is **462 cm^2**.