Here you get the CBSE Class 10 Mathematics chapter 11, Areas Related to Circles: NCERT Exemplar Problems and Solutions (Part-IVA). This part of the chapter is in continuation with Part-IVA for the same chapter that included solutions to first 7 questions from Exercise 11.4 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Areas Related to Circles. Here you will get solutions to next 7 questions, i.e., from Q. No. 8 to 14. Each solution is designed in an easy manner to make you understand the concept, easily.

**CBSE Class 10 Mathematics Syllabus 2017-2018**

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:**

**Exercise 11.4**

**Long Answer Type Questions (Q. No. 8-14)**

**Question. 8 **Find the area of the sector of a circle of radius 5cm, if the corresponding arc length is 3.5cm.

**Solution.**

Given a sector of a circle of radius (*r*) 5cm and its corresponding arc length (*l*) being 3.5 cm.

**Question.**** 9 **Four circular cardboard pieces of radii 7cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.

**Solution.**

Given, four circular cardboard pieces of radii (*r*) 7cm are joined together as shown below:

Also,* AP* and *DP* are radii at contact point* P*. So,* AD* will be perpendicular to the tangent through *P*. It implies that interior angles of quadrilateral are 90° each.

Also, area of square *ABCD = *(Side)^{2} = (14)^{2} = 196cm^{2}

Thus, area of shaded region = Area of square *ABCD* *-** *Area of four sectors = 196 - 154 = 42cm^{2}

**Question.**** 10 **On a square cardboard sheet of area 784cm^{2}, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular

plates. Find the area of the square sheet not covered by the circular plates.

**Solution.**

Let each side of square be *a* cm long and radius of each circular plate be *r* cm.

**Question.**** 11 **Floor of a room is of dimensions 5m ´ 4m and it is covered with circular tiles of diameters 50cm each as shown in figure. Find area of floor that remains uncovered with tiles, (use *π *= 3.14)

**Question.**** 12 **All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 1256

cm^{2}, (use *π = *3.14)

**Solution.**

Let *A*, *B*, *C *and *D* be the vertices of rhombus lying on a circle.

Let the radius of the circle be *r.*

**Question.**** 13 **An archery target has three regions formed by three concentric circles as shown in figure. If the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of three regions.

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**Question.**** 14 **The length of the minute hand of a clock is 5cm. Find the area swept by the minute hand during the

time period 6:05am and 6:40am.

**Solution.**

Area swept by the minute hand while moving from 6:05am to 6:40am is in the form of a sector of acircle with radius 5 cm.

i.e., Rdius, *r* = 5 cm

And, time swept by min hand = (6 : 40 am – 6 : 05 am) = 35 min.

Now, angle revolved by the minute hand in 60 minutes = 360°

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