Question

A rectangular sheet of cardboard us 4 cm by 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)

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

Dimension of card board is 4 cm and 2 cm

Then area of cardboard =$4\times 2=8$ sq cm

Since the least dimension=2 cm

The greatest possible circle can be have diameter of maximum 2 cm

So radius =$\frac{d}{2}=\frac{2}{2}=1$ cm

Then area of circle=$\pi r^2=\pi (1{)}^2=\pi$ sq cm

So remaining area=$(8-\pi )$ sq cm