RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 25 of Exercise 18A

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

25

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm × 7 cm. Find the area of the remaining cardboard.

Given:

Length of the rectangular cardboard = 14 cm


Breadth of the rectangular cardboard = 7 cm


Ques25.bmp


Area of rectangle = length × breadth


Area of cardboard = 14 × 7 = 98 cm2


Let the two circles with equal radii and maximum area have a radius of ‘r’ cm each.


Then, 2r = 7


r = cm


Area of circle = πr2


Area of two circular cut outs = 2 × πr2


= 2 × × ×


= 11 × 7 = 77 cm2


Thus, the area of remaining cardboard = 98 – 77 = 21 cm2


Hence, the area of remaining cardboard is 21 cm2.


Chapter Exercises

More Exercise Questions