A student takes a rectangular piece of paper 30 cm long and 21 cm wide. Find the area of the biggest circle that can be cut out from the paper. Also find the area of the paper left after cutting out the circle.

From figure,

Let ABCD be the rectangular piece.

Area of rectangular piece = 30 × 21 = 630 cm²

From figure,

Radius of the biggest circle that can be cut from the rectangular piece = $\dfrac{21}{2}$ = 10.5 cm

Area of circle = πr²

= $\dfrac{22}{7} \times (10.5)^2$

= $\dfrac{22}{7} \times 110.25$

= 22 × 15.75

= 346.5 cm².

Area of paper left = Area of rectangular piece - Area of circle

= 630 - 346.5

= 283.5 cm².

Hence, the area of the biggest circle that can be cut from the rectangular piece = 346.5 cm² and area of remaining paper = 283.5 cm².