Here you get the CBSE Class 10 Mathematics chapter 11, Areas Related to Circles: NCERT Exemplar Problems and Solutions (Part-IIIB). This part of the chapter is in continuation with Part-IIIA for same chapter that included solutions to first 8 questions from Exercise 11.3 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Areas Related to Circles. Here you will get solutions to remaining questions i.e., from Q. No. 9-16. Each solution is designed in an easy manner to make you understand the concept behind, easily.
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:
Short Answer Type Questions (Q. No. 9-16)
Question. 9 Find the area of the shaded region in figure.
Given diagrams can be represented as a combination of two triangles (inner and outer) and two semi-circles as shown below:
Question. 10 Find the area of the minor segment of a circle of radius 14cm, when the angle of the corresponding sector is 60°.
Hence, the required area of the minor segment is 17.796 cm2.
Question. 11 Find the area of the shaded region in figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-point P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD. (use π = 3.14)
Given diagram is a combination of four quadrants and a square of side 12 cm.
As, P is a mid-poinl of AB.
Question. 12 In figure arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm, To intersect the sides BC, CA and AB at their respective mid-points D,E and F. Find the area of the shaded region. (use π = 3.14)
Given diagram is a combination of three sectors and an equilateral triangle of side 10 cm.
In equilateral triangle ABC,
Question.13 In figure, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region.
Given, radii of each arc, r = 14cm
Let θ1, θ2 and θ3 be the three angles of ΔPQR.
Hence, the required area of the shaded region is 308cm2
Question. 14 A circular park is surrounded by a road 21m wide. If the radius of the park is 105m, then find the area of the road.
Given, radius of circular park, r = 105 m
Width of road around the park = 21m
Therefore, radius of bigger circle (park + road), R = 105 + 21 = 126m
Question.15 In figure, arcs have been drawn of radius 21cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.
Hence, required area of the shaded region is 1386cm2.
Question. 16 A piece of wire 20cm long is bent into the form of an arc of a circle, subtending an angle of 60° at its centre. Find the radius of the circle.
Given that length of arc of circle made from wire, l = 20cm
And central angle, θ = 60°