Question

Two goats are tethered to diagonally opposite vertices of a field formed by joining the mid-points of the adjacent sides of another square field of side 20√2m. What is the total grazing area of the two goats if the length of the rope by which the goats are tethered is 10√2 m

Answer 1

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Answer 2

Given:

The goat are tethered to the vertices.

The field is formed by joining the midpoint of 2 adjacent squares.

The length of the rope is 10√2 m.

To FInd:

The area that the goats can graze.

Explanation:

The field is formed by joining the midpoint of 2 adjacent squares

⇒ The field that the goats are in is also a square.

The goat are tethered to the vertices

⇒ The maximum area that the rope can cover is a quadrant of a circle.

Solution:

Find the area one goat can cover:

$\text{Area of one quadrant} = \dfrac{1}{4}\pi r^2$

$\text{Area of the quadrant} = \dfrac{1}{4}\pi (10\sqrt{2} )^2$

$\text{Area of the quadrant} = \dfrac{1}{4}\pi \times 200$

$\text{Area of the quadrant} =50\pi \text{ m}^2$

Find the area two goat can cover:

$\text{Area of the quadrant} =50\pi \text{ m}^2$

$\text{Area of 2 quadrants} =50\pi \times 2$

$\text{Area of 2 quadrants} =100\pi \text{ m}^2$

Answer: The total grazing area is 100π m²