Dear Reader, Below are three simple questions based on geometry. These are extremely easy questions.
There is a garden square in shape with its sides measuring 17 m. A cow aged 3 years old is tied to one of the corners of this square garden with a rope of 14 m. In this garden grass is available in plenty and the cow wanted to graze as much as possible. What is the area of this garden which the cow can graze comfortably?
a) 123 sq. m b) 154 sq. m c) 194 sq.m d) 204 sq.m.
Answer : b) 154 sq.m
Imagine the square garden – with sides measuring 17 m.
In one of its corners, this is cow tied with a rope of 14 m.
Normally when a cow is tied to a place with the rope it can graze in a full circle space.
Here since it has been tied to a corner of the square the cow can graze ¼ of circle space coverable with the rope tied.
Area of circle = 22/7 x r x r where r is the radius of the circle.
Here the radius is 14 m.
So area where cow can graze = Area of circle / 4 = ( 22/7 x 14 x 14 )/ 4 = 154 sq.m
NOTE: Some of us may be tempted to calculate taking circumference of circle in mind i.e. 2 x 22/7 x r. The cow can graze not only the outer area but also inside the quadrant.(quarter circle)
Two goats are tied in the diagonally opposite corners of a square graze yard of size 54 m with two ropes of 21 m length. What is the area of the graze yard that can be grazed by the two goats put together?
a) 693 sq. m. b) 346 ½ sq.m. c) 1386 sq.m. d) none of these.
Answer : a) 693 sq.m.
Think of the square ground with side at 54 m.
In the problem it is given one goat is tied to a corner of square ground with rope of 21 m length. In the same way another goat is tied to the diagonally opposite corner with another rope of 21 m length.
Area of circle = 22/7 x r x r where r is the radius.
In the case of a goat tied to a corner of a ground , it can graze 1/4 of the circle that can be made with the length of the rope tied. (quadrant)
In this problem two goats are tied at two diagonally opposite corners of the ground with ropes of 21 m each. So these two can graze area of circle /2
(22/7 x 21 x 21)/2 = 693 sq.m
Bengaluru city has an excellent small garden rectangle in shape with its length measuring 283 m and breadth 150 m in Malleswaram area. An owner of a goat brought his goat and tied it at a corner of the garden with a rope of 112 m length. He wanted his goat to graze all that area that can be covered by it with the rope tied. Please ascertain and tell him the area of garden which his goat will not be able to graze?
a) 38956 sq.m. b) 35896 sq. m. c) 36598 sq.m. d) 32594 sq,m
Answer : d) 32594 sq. m.
Though the question says the garden is rectangular, still the graze area would be a quarter of a circle as can be seen from the figure below.
In that the goat is tied in one corner of the ground with a rope of 112 m
Area of land the goat can graze = (22/7 x r x r)/4 where r is the length of the rope.
So, (22/7 x 112 x 112) / 4 = 9856 sq. m ...(1)
But the question is on the area that goat cannot graze at all.
Area where goat cannot reach = Area of rectangle - Graze area = Length x Breadth - Graze Area
Apply length = 283m and breadth = 150m. Also we know graze area = 9856 sq. m from (1)
Therefore area that cannot be reached by goat = 283 x 150 - 9856 = 42450 - 9856 = 32594