Dear Reader,
Below are three easy questions dealing with circles, distances and their areas etc.
Question 1
Venkatanarayana Road, T.Nagar, Chennai 600017 has a playground that is circular in shape. Mukesh started running in clock wise direction from point X. Anil started running from point X in anti-clockwise direction. Mukesh ran 550 m and Anil ran 330 m before they met each other. What is the area of this ground?
a) pi x 16.9 x 102 m2 b) pi x 1.97 x 102 m2 c) pi x 19.6 x 102 m2 d) pi x 1.69 x 102 m2
Answer : c) pi x 19.6 x 102 m2
Solution :
Circumference of a circle = 2 x 22/7 x radius
Mukesh has run 550 m and Anil has run 330 m before they met. So the circumference of the circle would be the sum of the distances they covered = 550 m + 330 m = 880 m.
Circumference = 880 m = 2 x 22/7 x R
R = 880 x 7 divided by 2 x 22 = 140 m.
Area = pi x R2 = pi x 19.6 x 102
Question 2
Cubbon Park, Bangalore has a circular garden inside it constructed hundreds of years ago. Bangalore Corporation has been maintaining this garden nicely. Many people – retired persons, young persons go for jogging around this circular garden in the early mornings. The radius of the garden is 777 m. Rajendra Kumar and Nagendra Kumar are two close friends. One day they started jogging from a point on the border of circle—Rajendra Kumar went in anti clockwise direction and Nagendra Kumar went in clockwise direction. Nagendra Kumar met Rajendra Kumar after travelling 2416 Km lesser than that would had been covered by Rajendra Kumar. What is the distance covered by Rajendra Kumar before meeting Nagendra Kumar?
a) 3560 m b) 5360 m c)3650 m d)none of these.
Answer : c) 3650 m
Solutions :
Total circumference of the circular garden = 2 x 22/7 x 777 = 4884 m.
Let the distance covered by Nagendra Kumar when they met be X.
Let the distance covered by Rajendra Kumar when they met be Y.
It is given that Y - X = 2416 -> eq 1
Also we know that sum of the distances covered by both the friends should be equal to the circumference of the circle
Therefore Y + X = 4884 -> eq 2
Adding equations 1 and 2 we get 2Y = 7300
Therefore Y = 7300 / 2 = 3650.
Hence, Distance covered by Rajendra Kumar = 3650 m
Question 3
There is a circular garden in Mattuthavani, Madurai and is being maintained by a private transport company for many years. The radius of the ground is 1554 m. Gunaseelan and Munusamy started running from a point at the circumference in opposite directions. Gunaseelan ran at an average speed of 60 metres per minute and met Munusamy after running for 44 minutes. How much distance Munusamy would have covered before meeting Gunaseelan?
a) 7128 m b) 6128 m c) 5456 m d) none of these.
Answer : a) 7128 m
Solution :
Circumference of circular ground = 2 x 22/7 x 1554 m = 9768 m
Distance covered by Gunaseelan in 44 minutes travelling at 60 metres per minute = 60 x 44 = 2640 m
Let distance covered by Gunaseelan when they met = X. We have already found X to be 2640 m.
Let distance covered by Munusamy when they met = Y.
Similar to previous question, we have X + Y = Circumference
2640 + Y = 9768
Distance covered by Munusamy = Y = 9768 - 2640 = 7128 m