Question

A circle of largest area is cut from a rectangular piece of card-board with dimension $55cm$ and $42cm$. Find the ratio between the area of the circle cut and the area of the remaining card-board.

• A. $3:2$
• B. $6:4$
• C. $13:2$
• D. $3:12$

Answer 1

Answer: (A), (B)

The correct options are
A $3:2$
B $6:4$

The largest area of the circle is possible when diameter $42cm$
Therefore,
Radius=$\frac{42}{2}=21cm$
Therefore,
Area of circle $=\pi (21{)}^2$$=1386c{m}^2$
Area of rectangle $=(42\times 55)cm$$=2310c{m}^2$
Therefore,
Area of remaining cardboard $=42\times 55-\pi (21{)}^2$
$=2310-1386$
$=924c{m}^2$
Therefore,
Ratio of area of circle and area of remaining cardboard $=1386:924=3:2$