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A cow is placed for grazing inside a rectangular field $70 m b y 52 m$ . It is tethered to one corner by a rope of length $21 m$ .

The area that is left ungrazed is ____ $m 2$ .

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Detailed Solution

A cow is placed for grazing inside a rectangular field

70 m b y 52 m

. It is tethered to one corner by a rope of length

21 m

.
The area that is left ungrazed is 3293.5

m 2

.
Given, length is

70 m

and breadth is

52 m

.
The area of a rectangle is given as-

A r e a o f t h e r e c t a n g l e = l e n g t h × b r e a d t h

Therefore, the area of the rectangular field is-

= 70 × 52 = 3640 m 2

Given, length of the rope is

21 m

.
Therefore, the total area that can be grazed by the cow is given as-

π (l e n g t h o f t h e r o p e) 2 4 = 227 × 14 × 21 × 21 = 11 × 3 × 21 2 = 346.5 m 2

Now, the area that is left ungrazed by the cow is given as-

= Area of rectangular field − Area can be grazed = 3640 − 346.5 = 3293.5 m 2

Hence,

3293.5 m 2

is the required area.

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