PROBLEMS ON AREA RELATED TO CIRCLES WORKSHEET

Problem 1 :

If the circumference and the area of a circle are numerically equal, then the radius of the circle is-

(a) 4 units      (b) π units      (c) 2 units      (d) 7 units

Solution

Problem 2 :

The radius of a circle is 50 cm. If the radius is decreased by 50%, its area will be decreased by-

(a) 50%     (b) 75%     (c) 80%       (d) 25%

Solution

Problem 3 :

If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then-

a) R₁ + R₂ = R          b) R₁² + R₂2 = R²       c)  R₁ + R₂ < R

d)  R₁² + R₂2 < R²

Solution

Problem 4 :

The areas of two concentric circles forming a ring are 154 square cm and 616 square cm. The breath of the ring is 

Solution

Problem 5 :

The circumference two circles are in the ratio 4:9. Find the ratio of their area. 

Solution

Problem 6 :

Find the area of a right- angled triangle if the radius of its circumcircle is 2.5 cm and the altitude drawn to the hypotenuse is 2 cm long

Solution

Problem 7 :

The minute hand of a clock is 10 cm long. Find the area of the face of the clock described by the minute hand between 8 a.m. and 8:25 a.m.

Solution

Problem 8 :

The diameter of a circular pond is 17.5 cm. It is surrounded by a path of width 3.5 m. Find the area of the path.

Solution

Problem 9 :

A steel wire when bent in the form of a square encloses an area of 121 sq. cm. If the same wire is bent into the form of a circle, find the area of the circle

Solution

Problem 10 :

If the area of the circle is 154 cm², its perimeter is 

Solution