Discussion
A wooden rectangular plank has dimensions 12m and 6 m. Three circular portions are cut from the plank having diameters 2m, 2m and 1m.How much area of the plank remains?
Answer: D
Halve each diameter to get the radii: 1 m, 1 m and 0.5 m.
\[ A_{\text{plank}} = 12 \times 6 = 72 \text{ m}^{2} \]
\[ A_{\text{holes}} = \pi(1)^{2} + \pi(1)^{2} + \pi(0.5)^{2} = \pi + \pi + \frac{\pi}{4} = \frac{9\pi}{4} \]
\[ A_{\text{remaining}} = 72 - \frac{9\pi}{4} = \frac{288 - 9\pi}{4} \text{ m}^{2} \]
Numerically that is about 64.93 m². Using the diameters directly in \( \pi r^{2} \) would quadruple the holes' area.
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