Here you get the CBSE Class 10 Mathematics chapter 11, Areas Related to Circles: NCERT Exemplar Problems and Solutions (Part-IVC). Here you will get solutions to Q. No. 15-20 from exercise 11.4 of NCERT Exemplar Problems for Class 10 Mathes. Each solution is designed in an easy manner to make you understand the concept, easily. For questions numberd 1-14, cisit the links given below.
NCERT Exemplar problems are a very good resource for preparing the critical questions like Higher Order Thinking Skill (HOTS) questions. All these questions are very important to prepare for CBSE Class 10 Mathematics Board Examination 2017-2018 as well as other competitive exams.
Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Areas Related to Circles:
Long Answer Type Questions (Q. No. 15-20):
Question. 15 Area of a sector of central angle 200° of a circle is 770cm2. Find the length of the corresponding arc of this sector.
Let r be the radius of the circle.
Given, central angle of sector, q = 200°
And, area of sector = 770 cm2
Question. 16 The central angles of two sectors of circles of radii 7cm and 21cm are respectively 120° and 40°. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe?
Given, radius of first sector, r1 = 7cm
And central angle of first sector, θ1 = 120°
Also, radius of second sector, r2 = 21cm
And central angle of second sector, θ2 = 40°
Hence, we observe that arc lengths of two sectors of two given circles are equal but area of second circle is three times that of the first circle.
Question. 17Find the area of the shaded region given in figure.
Given figure is a combination of 4 semi circles, JHM, MGL, LFK and KEJ and two squares JMLK and ABCD.
Question. 18 Find the number of revolutions made by a circular wheel of area 1.54m2 in rolling a distance of 176m.
Hence, the required number of revolutions made by the circular wheel is 40.
Question. 19 Find the difference of the areas of two segments of a circle formed by a chord of length 5cm subtending an angle of 90° at the centre.
Chord AB = 5 cm subtending an angle of 90° at the centre, divides the circle in two segments minor segment ACB and major segment ADB.
Question. 20 Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm.
Given, radius of the circle, r = 21cm
Hence, the required difference in areas of two sectors of given circle is 462 cm2.