How many circular plates of diameter d be taken out of a square plate of side 2d with minimum loss of material?

Area of square plate = \( \Large (Side)^{2} \)

= \( \Large (2d)^{2}=4d^{2} \)

Area of circular plate = \( \Large \pi \left(\frac{d}{2}\right)^{2}=\frac{\pi d^{2}}{4} \)

Number of square plates

=\( \Large \frac{4d^{2}}{\frac{\pi d^{2}}{4}}=\frac{4\times 4}{\pi} \)=5

Since, nearest integer value is 5.