Question

A cow is tied with a rope in the middle of a circular grass field of radius 14m. It
started grazing around the boundary and completed 3⁄4 of the field. What is the
distance covered and displacement of the cow?

Answer 1

Answer

A cow is tied with a rope of length 14m at the corner of rectangular field of dimesions 20m x 16m, find area of field in

Area grazed by cow

=

4

1

th

area of circle

=

4

πr

2

=

4

3.14×14×14

=153.86m

2

∴ Area grazed by cow

=153.86m

2

Answer 2

The distance covered and displacement of the cow $=154 \mathrm{~cm}^{2}$.

• Let us suppose the rectangular field to be A B C D and the cow is tied at corner B.
• Then, we can observe that the cow can graze in the quadrant of circular region having radius equals to 14m.
• So, the area of the field in which the cow can graze is equal to the area of the quadrant.

What is area of quadrant?

• The area of a circle, A=πr2.
• Now, to calculate the area of a quadrant, divide the area of a circle by 4 (as four quadrants make a circle).
• We get, Area of a quadrant, A= (πr2)/4 Square units.

According to the question:

We know that, Area of quadrant $=\frac{\pi r^{2}}{4}$.

Where,r is the radius of the quadrant.

We have r=14 m.

Area of quadrant $=\frac{\pi(14)^{2}}{4}$.

Substituting the value of $\pi=\frac{22}{7}$ we get,

Area of quadrant $=\frac{22}{7} \times \frac{14 \times 14}{4}$

$=154 \mathrm{~cm}^{2}$.

Hence, The distance covered and displacement of the cow $=154 \mathrm{~cm}^{2}$.

Learn more about area of quadrant here,

https://brainly.in/question/85794?msp_poc_exp=5

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