Question

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

• A. $3:2$
• B. $5:2$
• C. $7:2$
• D. $7:8$

Answer 1

The correct option is A $3:2$

The largest area of the circle is possible when,
diameter $=$ $42$
Therefore, radius $=$ $\frac{42}{2}$ $=$ $21$ cm
Therefore,
Area of circle $=$ $\pi (21{)}^2$
$=$ $1386$
Area of rectangle $=$ $(42\times 55)cm$ $=$ $2310$
Therefore, area of remaining cardboard $=$ $42\times 55-\pi (21{)}^2$
$=$ $2310-1386$
$=$ $924$
Therefore, ratio of area of circle and arc of remaining cardboard $=$ $1386:924$
$=$ $231:154$
$=$ $33:22$
$=$ $3:2$