Areas Related to Circles
Exercise 12.1
Question 4:
The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?
Sol.
Diameter of the wheel of the car = 80 cm
Radius (r) of the wheel of the car = 40 cm
Circumference of wheel = 2πr
= 2π (40) = 80π cm
Speed of car = 66 km/hour
Distance travelled by the car in 10 minutes
= 110000 × 10 = 1100000 cm
Let the number of revolutions of the wheel of the car be n.
n × Distance travelled in 1 revolution (i.e., circumference)
= Distance travelled in 10 minutes
Therefore, each wheel of the car will make 4375 revolutions.
Question 5:
Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(A) 2 units (B) π units (C) 4 units (D) 7 units
Let the radius of the circle be r.
Circumference of circle = 2πr
Area of circle = πr2
Given that, the circumference of the circle and the area of the circle are equal.
This implies 2πr = πr2
2 = r
Therefore, the radius of the circle is 2 units.
Hence, the correct answer is A.