Question

A rope by which a calf is tied is increased from 12m to 23m . how much additional grassy ground shall it graze


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Answer 1

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Answer 2

Given:

Length of the rope=12m

Increased length=23m

To find:

The additional ground grazed

Solution:

The additional grassy ground grazed by the calf is 1,210m².

We can find the area by following the steps given below-

We know that a calf is tied by a rope to one point. The area that can be grazed by the calf will be the area of the circle whose radius is equal to the length of the rope.

The area of a circular area=πr², where r is the radius.

The length of the rope, radius, r=12m

The area grazed by the calf=π×12×12

=144πm²

Now, the length of the rope has been increased to 23m.

So, the new radius, R=23m

The area covered by the calf with increased length of rope=πR²

=π×23×23

=529πm²

The additional area grazed is the difference between the area grazed with the original rope and the area grazed with the longer rope.

The additional area= πR² -πr²

On putting the values, we get

=529π-144π

=385π

=385×22/7

=55×22

=1,210m²

Therefore, the additional grassy ground grazed by the calf is 1,210m².