A cone of height 7 cm and base radius 3 cm is carved from a rectangular block of wood 10 cm × 5 cm × 2 cm. The percentage of wood wasted is:

1. 34%

2. 46%

3. 54%

4. 66%

Volume of rectangular block = 10 cm × 5 cm × 2 cm = 100 cm³

Volume of cone = $\dfrac{1}{3}π \text{r}^2 \text{h}$

$= \dfrac{1}{3} \times \dfrac{22}{7} \times 3^2 \times 7 \\[1em] = \dfrac{1}{3} \times 22 \times 9 \\[1em] = 22 \times 3 \\[1em] = 66 \text{ cm}^3.$

Volume of wood wasted = Volume of rectangular block - Volume of cone

= 100 - 66

= 34 cm³

Percentage of wood wasted

= $\dfrac{\text{Volume of wood wasted}}{\text{Total volume of rectangular block}} \times 100 = \dfrac{34}{100} \times 100$ = 34%

Hence, option 1 is the correct option.