Question

A horse is tethered at one corner of a square shaped grass field of side 21m by means of a 7m long rope. Find the ungrazed area.

Answer 1

» To Find :

The Area of the Square field , which is not eaten by the Horse.

» Given :

• Side of the Square = 21 m

• Length of the Rope = 7 m

» We Know :

Area of a Square :

$\sf{\underline{\boxed{A = (a)^{2}}}}$

Where , a is the side of the Square.

Area of a Circle :

$\sf{\underline{\boxed{A = \pi r^{2}}}}$

Where , r is the Radius of the circle .

» Concept :

According to the question , it said that the inside the square field ,the horse was tied with a rope from the end of the corner.

Since the rope was tied at the end of the corner , then we can say it is the radius of a Circle , so the difference of the Area of the Square and the Area of the grazed will give the Area of the field ungrazed by the Horse.

$\therefore$ Area of Square - Area of Circle = Area of ungrazed field.

» Solution :

Area of Square :

• side= 21 m

Using the formula and substituting the values in it ,we get :

$\sf{\underline{\boxed{A = (a)^{2}}}}$

$\sf{\Rightarrow A = (21)^{2}}$

$\sf{\Rightarrow A = 441 m^{2}}$

Hence , the area of the Square field is 441 m².

Area of the grazed part :

• Radius = 7 m

Using the formula and substituting the values in it ,we get :

$\sf{\underline{\boxed{A = \pi r^{2}}}}$

$\sf{\Rightarrow A = \dfrac{22}{7} \times 7^{2}}$

$\sf{\Rightarrow A = \dfrac{22}{7} \times 49}$

$\sf{\Rightarrow A = \dfrac{22}{\cancel{7}} \times \cancel{49}}$

$\sf{\Rightarrow A = 22 \times 7}$

$\sf{\Rightarrow A = 154 m^{2}}$

Hence , the Area of the grazed part is 154 m².

Area ungrazed by the horse :

Area of Square field - Area of grazed part

$\sf{\Rightarrow 441 - 154}$

$\sf{\Rightarrow 287 m^{2}}$

Hence, the area ungrazed by the Horse is 287 m²

» Additional information :

• Area of a Sector = lh/2

• Perimeter of a Sector = l + 2r

• Volume of a Sphere = 4/3πr³.

• Volume of a hemisphere = ⅔πr²