Question 1
A horse is tied to a pole by a rope of length 21m. If the length of the rope is increased to 28m, then how much excess area will it be able to graze?
a) 1386 m2 b) 1078 m2 c) 2464 m2 d) 1378 m2
Answer : b) 1078 m2
Solution :
Let r and R be the original and new proposed lengths of the rope respectively.
Given r = 21 m and R = 28 m.
Area of the surface with radius r = π x r2 = 22/7 * 21 * 21 m2 = 1386 m2
Area of the surface with radius R = π * R2 = 22/7 * 28 * 28 m2 = 2464 m2
Therefore, Additional area for grazing if length is increased = 2464 – 1386 m2 = 1078 m2
Question 2
A cow was tied in the middle of the circular field by a rope of length 70 ft to graze the field. If the area of the circular field is 20000 sq.ft, then what is the area of the field that is not accessible to the cow?
a) 1540 sq.ft b) 6400 sq.ft c) 4600 sq.ft d) 1450 sq.ft
Answer : c) 4600sq.ft
Solution :
The length of the rope is 70 ft
The area grazed by the cow = π x 70 x 70 sq.ft = 15400sq.ft
Given that the area of the circular field = 20000ft
Then, the area of the field not accessible to the cow = 20000sq.ft – 15400sq.ft = 4600 sq.ft
Question 3
A man bought a field of length 250 m and breath 200 m. He planned to build a house of area 37500 m2. And in the remaining area he planned to cultivate wheat crop. What is the length of the cultivating area if the breadth is 50m?
a) 150m b) 250m c) 350 m d) 200m
Answer : b) 250m
Solution :
Area of the field, he bought = 250 x 200 m2 = 50000 m2
Given that the area of the house = 37500 m2
Then the remaining area = 50000 m2 – 37500 m2 = 12500 m2
Also given that the breadth of the remaining area = 50 m
Then the length of the cultivating area = 12500 / 50 = 250 m