A rope by which a cow is tethered is increased from 16 m to 23 m. How much additional ground does it have now to graze?
Here the increase in the length of the rope simply means that there is increase in the radius of the circle within which cow can graze. Now to find the additional area available for grazing can be easily be found by simply subtracting the initial area available for grazing from the new area available.
Initial radius = r = 16 cm
Increased radius = R = 23 cm
Additional ground available = Area of new ground – Initial area → eqn1
Initial area of ground = π(r2)
⇒ Initial area of ground = π(162)
⇒ Initial area of ground = 256π → eqn2
Area of new ground = πR2
⇒ Area of new ground = π(232)
⇒ Area of new ground = 529π → eqn3
Now put the values of equation 2 and 3 in equation 1
⇒ Additional area of ground available = 529π – 256π
⇒ Additional area available = (529 – 256)π (Taking π common)
⇒ Additional ground available = 273π
= 858 cm2
The additional ground available is 858 cm2.