Question

A rectangular sheet of cardboard is $4$ cm $\times$ $2$ cm. The greatest possible circle is cut off from the cardboard, then the remaining area is:

• A. $(16-\pi )c{m}^2$
• B. $(16-4\pi )c{m}^2$
• C. $(8-\pi )c{m}^2$
• D. $(8-4\pi )c{m}^2$

Answer 1

Answer: (C)

$(8-\pi )c{m}^2$

Area of card board $=2\times 4=8{cm}^2$

Least dimension is $2cm$, the greatest possible circle have a diameter of maximum $2cm$.

$\therefore$ Radius $=1cm$

Area of remaining part $=8-(\pi \times 1^2)=(8-\pi ){cm}^2$