Priyanka took a wire and bent it to form a circle of radius 14 cm. Then she bent it into a rectangle with one side 24 cm long. Then choose the option which represents the length of the wire and the figure which encloses more area among the two.

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66 cm, circle

77 cm rectangle

88 cm, circle

99 cm, rectangle

answer is C.

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Detailed Solution

Given as follows,
Priyanka took a wire and bent it to form a circle of radius =14 cm
Afterwards when she bent it into a rectangle, one of its side length = 24 cm
As the wire is bent to form a circle, so the total length of the wire will be the circumference of the circle.
Now, as the circumference of a circle of radius ‘r’ is given as

2 π r

, so, we have the total length ‘l’ of the wire as follows,

l = 2 π r l = 2 × 227 × 14 l = 88 cm

Next, the area of a circle is given as

π r 2

, so the area of the circular wire will be,

= 227 × 142 = 616 cm 2

So, the area of the wire bent as a circle is obtained as

616 cm 2

.
Next, the same wire is bent in the form of a rectangle with one side measure as 24 cm, so the length of the wire will be the perimeter of the rectangle.
Now, as the perimeter of a rectangle with length ‘L’ and breadth ‘B’ is given by