Question

A goat is tethered to the center of a square field of side 20metre by a rope 10metre
long . Find what fraction of the grass on the field the goat is able to eat ( take πto be 22/7)​

Answer 1

Given :-

• side of square field , s = 20 m
• goat is tethered to the center of field
• length of rope = 10 m

To find :-

↪ Fraction of grass on the field goat is able to eat

Formula used :-

◆ Area of square = ( side )²   sq. units

◆ Area of circle = π × ( radius )²  sq. units

Solution :-

Finding the area of square field

→  ar ( square field ) = ( side )²

→ ar ( square field ) = ( 20 )²

→ ar (square field )= 400  m²

Finding the area of circle of radius 10 cm (where goat could graze)

→ ar ( circle ) = π × ( radius )²

→ ar ( circle ) = $\sf{\frac{22}{7}\times(10 )\times(10)}$

→ ar ( circle ) =  $\sf{\frac{2200}{7}\;\;m^2}$   (approx.)

Finding the fraction of grass on the field goat is able to eat

→   $\sf{\frac{ar(circle)}{ar(square\:field)}}$

→ $\sf{\frac{\frac{2200}{7}}{400}}$

→ $\boxed{\large{\sf{\frac{11}{14}}}}\;Ans.$