Important Questions for Chapter 12 - Areas Related to Circles

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Important questions based on NCERT syllabus for Chapter 12 - Areas Related to Circles:

Question 1: In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.
surface
Solution:
All the four circles are congruent.
Therefore, unshaded area of the square is equal to one full circle with radius 7 cm.
Area of square
= 142 = 196 cm^2

Area of circle
=π(7)2 = 153.86 cm^2

Area of shaded portion
= 196 − 153.86

= 42.14 cm^2

Question 2: The cost of fencing a circular field at the rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per m^2. Find the cost of ploughing the field in Rupees. (Take π = 22/7).
Solution:
Length of the fence (in meters)
= Total cost/Rate = 5280/24 = 220
So, circumference of the field = 220 m
Therefore, if r meters is the radius of the field, then
2πr = 220
2 × 22/7 × r = 220
r = 220 × 7/22 × 2 = 35
i.e., radius of the field is 35 m.
Therefore, area of the field
= πr^2 = 22/7 × 35 × 35 = 22 × 5 × 35 m^2
Now, cost of ploughing 1 m2 of the field = Rs. 0.50
So, total cost of ploughing the field
= Rs. 22 × 5 × 35 × 0.50 = Rs.1925

Question 3: In Akshita’s house there is a flower pot. The sum of radii of circular top and bottom of a flowerpot is 140 cm and the difference of their circumference is 88 cm. Find the diameter of the circular top and bottom.
Solution:
Diameter on top = R
Radius of bottom = r
R + r = 140 cm….(1)
2πR − 2πr = 88cm
R − r = 88/2π = 14 ….(2)
Adding (1) and (2),
2R = 154
R = 77
r = 140 − 77 = 63
Thus diameter of top will be 154cm and diameter of bottom is 126cm