SolveItClass 10 · NCERT

NCERT Solutions · Class 10 Mathematics Areas Related to Circles

14 questions · 14 still being checked

EXERCISE 11.1 1–10 (part 1 of 2)

  1. Unless stated otherwise, use \(\displaystyle \pi=\frac{22}{7}\).

    Exercise 1

    Find the area of a sector of a circle with radius 6\displaystyle 6 cm if angle of the sector is 60\displaystyle 60°.
    NCERT’s answer
    $\displaystyle \frac{132}{7} \mathrm{~cm}^{2}$

    Working being prepared

  2. Exercise 2

    Find the area of a quadrant of a circle whose circumference is 22\displaystyle 22 cm.
    NCERT’s answer
    $\displaystyle \frac{77}{8} \mathrm{~cm}^{2}$

    Working being prepared

  3. Exercise 3

    The length of the minute hand of a clock is 14\displaystyle 14 cm. Find the area swept by the minute hand in 5\displaystyle 5 minutes.
    NCERT’s answer
    $\displaystyle \frac{154}{3} \mathrm{~cm}^{2}$

    Working being prepared

  4. Exercise 4

    A chord of a circle of radius 10\displaystyle 10 cm subtends a right angle at the centre. Find the area of the corresponding:
    (i)
    minor segment
    (ii)
    major sector. (Use π=3.14\displaystyle \pi=3.14 )
    NCERT’s answer
    (i)
    $\displaystyle 28.5 \mathrm{~cm}^{2}$ (ii) $\displaystyle 235.5 \mathrm{~cm}^{2}$

    Working being prepared

  5. Exercise 5

    In a circle of radius 21\displaystyle 21 cm, an arc subtends an angle of 60\displaystyle 60° at the centre. Find:
    (i)
    the length of the arc
    (ii)
    area of the sector formed by the arc
    (iii)
    area of the segment formed by the corresponding chord
    NCERT’s answer
    (i)
    $\displaystyle 22$ cm (ii) $\displaystyle 231 \mathrm{~cm}^{2}$ (iii) $\displaystyle \left(231-\frac{441 \sqrt{3}}{4}\right) \mathrm{cm}^{2}$

    Working being prepared

  6. Exercise 6

    A chord of a circle of radius 15\displaystyle 15 cm subtends an angle of 60\displaystyle 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π=3.14\displaystyle \pi=3.14 and 3=1.73\displaystyle \sqrt{3}=1.73 )
    NCERT’s answer
    $\displaystyle 20.4375 \mathrm{~cm}^{2} ; 686.0625 \mathrm{~cm}^{2}$

    Working being prepared

  7. Exercise 7

    A chord of a circle of radius 12\displaystyle 12 cm subtends an angle of 120\displaystyle 120° at the centre. Find the area of the corresponding segment of the circle. (Use π=3.14\displaystyle \pi=3.14 and 3=1.73\displaystyle \sqrt{3}=1.73 )
    NCERT’s answer
    $\displaystyle 88.44 \mathrm{~cm}^{2}$

    Working being prepared

  8. Exercise 8

    A horse is tied to a peg at one corner of a square shaped grass field of side 15\displaystyle 15 m by means of a 5\displaystyle 5 m long rope (see Fig. 11.8\displaystyle 11.8). Find
    (i)
    the area of that part of the field in which the horse can graze.
    (ii)
    the increase in the grazing area if the rope were 10\displaystyle 10 m long instead of 5\displaystyle 5 m. (Use π=3.14\displaystyle \pi=3.14 )
    NCERT_Question_Class10_Maths_Ch11_Ex11-1_Q8
    NCERT’s answer
    (i)
    $\displaystyle 19.625 \mathrm{~m}^{2}$ (ii) $\displaystyle 58.875 \mathrm{~cm}^{2}$

    Working being prepared

  9. Exercise 9

    A brooch is made with silver wire in the form of a circle with diameter 35\displaystyle 35 mm . The wire is also used in making 5\displaystyle 5 diameters which divide the circle into 10\displaystyle 10 equal sectors as shown in Fig. 11.9. Find :
    (i)
    the total length of the silver wire required.
    (ii)
    the area of each sector of the brooch.
    NCERT_Question_Class10_Maths_Ch11_Ex11-1_Q9
    NCERT’s answer
    (i)
    $\displaystyle 285$ mm (ii) $\displaystyle \frac{385}{4} \mathrm{~mm}^{2}$

    Working being prepared

  10. Exercise 10

    An umbrella has 8\displaystyle 8 ribs which are equally spaced (see Fig. 11.10\displaystyle 11.10). Assuming umbrella to be a flat circle of radius 45\displaystyle 45 cm, find the area between the two consecutive ribs of the umbrella.NCERT_Question_Class10_Maths_Ch11_Ex11-1_Q10
    NCERT’s answer
    $\displaystyle \frac{22275}{28} \mathrm{~cm}^{2}$

    Working being prepared