The radius of a hemispherical bowls is $6\text{cm}$. The capacity of the bowl is $\left(\text{Take } \pi=\frac{22}{7}\right)$

### Concept & Formula The capacity of a bowl is synonymous with its internal volume. For a hemisphere, the volume is exactly half of a full sphere. $$ \text{Volume of Hemisphere} = \frac{2}{3}\pi r^3 $$ ### Step-by-Step Solution 1. **Given:** - Radius $r = 6\text{cm}$ - $\pi = \frac{22}{7}$ 2. **Apply the Formula:** - $\text{Volume} = \frac{2}{3} \times \frac{22}{7} \times (6)^3$ - $\text{Volume} = \frac{2}{3} \times \frac{22}{7} \times 216$ 3. **Simplify and Calculate:** - Divide $216$ by $3$ to get $72$. - $\text{Volume} = 2 \times \frac{22}{7} \times 72$ - $\text{Volume} = \frac{44 \times 72}{7} = \frac{3168}{7}$ 4. **Convert to Decimal:** - $3168 \div 7 = 452.5714...$ - Rounding to two decimal places, we get $452.57\text{ cm}^3$. ### Exam Strategy & Shortcut When multiplying $44 \times 72$, you can split it as $44 \times (70 + 2) = 3080 + 88 = 3168$. When dividing by $7$, notice that $7 \times 400 = 2800$ and $7 \times 50 = 350$, so the result must be slightly above $450$. Option (b) is the only reasonable match without fully completing the long division. ### Common Pitfall Using the formula for the volume of a full sphere ($\frac{4}{3}\pi r^3$) instead of a hemisphere, which would yield exactly double the correct answer. ### Final Answer Therefore, the correct answer is **$452.57\text{cm}^3$**.