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.
​

Answer 1

Answer:

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Answer 2

Answer:

3:2

Step-by-step explanation:

The largest area of the circle is possible when,

diameter = 42

Therefore, radius =   $\frac{42}{2}$ = 21 cm

Therefore,

Area of circle =π$r^{2}$

                      = π$(21)^{2}$

                      = 1386

Area of rectangle = (42×55)cm = 2310

Therefore, area of remaining cardboard = (42×55)−π$(21)^{2}$

                                                                   = 2310−1386

                                                                   = 924

Therefore, ratio of area of circle and arc of remaining cardboard = 1386:924

= 231:154

= 33:22

= 3:2