Question

16. A rope by which a calf is tied is increased from 12 m to 23 m. How muc it graze?​

Answer 1

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=r², where r is the radius.

The length of the rope, radius, r=12m The area grazed by the calf=π×12×12

=144m²

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

=πX23x23

=529m²

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=π R² -πr²

On putting the values, we get

=529T-144π

=385π

=385×22/7

=55x22

=1,210m²

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