Chapter 11 · Areas Related to Circles

NCERT Exemplar Class 10 Maths Exercise 11.3

All 16 questions of NCERT Exemplar Class 10 Maths Exercise 11.3 (Areas Related to Circles), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Find the ​radius of a circle ​whose circumference is equal to the ​sum of the circumferences of ​two circles ​of radii 15 ​cm and ​18 cm.
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   Radius $=33$ cm.

   Step-by-step solution →
2. Q2
   In Fig. 11.5, a ​square of diagonal 8 ​cm is inscribed in a ​circle. ​Find ​the area ​of the shaded ​region.

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   Area of the shaded region $=18.24$ cm${}^2$.

   Step-by-step solution →
3. Q3
   Find the area of a ​sector ​of ​a circle ​of radius ​28 cm and ​central ​angle $45^{\circ }$.
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   Area of the sector $=308$ cm${}^2$.

   Step-by-step solution →
4. Q4
   The ​wheel ​of ​a motor cycle is of radius 35 cm. ​How many revolutions ​per minute must the ​wheel make ​so as to keep a speed of 66 km/h?
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   The wheel must make $500$ revolutions per minute.

   Step-by-step solution →
5. Q5
   A ​cow ​is tied with a rope of ​length 14 m ​at the corner of a ​rectangular field of ​dimensions 20 m $\times$ 16 m. Find the area of the field in ​which ​the cow can graze.
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   The cow can graze an area of 154 m^2 (a quarter circle of radius 14 m).

   Step-by-step solution →
6. Q6
   Find the ​area ​of the flower bed (with semi-circular ​ends) shown in ​Fig. 11.6.

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   Area of the flower bed $=380+\frac{550}{7}=\frac{3210}{7}\approx 458.57$ cm${}^2$.

   Step-by-step solution →
7. Q7
   In Fig. ​11.7, $AB$ ​is a diameter ​of ​the circle, $AC=6$ cm and $BC=8$ cm. Find the ​area ​of the shaded ​region (Use $\pi =3.14$).

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   The area of the shaded region is $78.5-24=54.5{\text{cm}}^2$.

   Step-by-step solution →
8. Q8
   Find ​the area of the shaded field shown in ​Fig. 11.8. The field is a rectangle 8 m by 4 m with ​a semicircle ​attached ​below the left part of its ​lower side; on the ​left, from the top of the rectangle to the bottom of the semicircle, the field measures 6 m.

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   Shaded area $=(32+2\pi ){\text{m}}^2=\frac{268}{7}\approx 38.29{\text{m}}^2$ (taking $\pi =\frac{22}{7}$).

   Step-by-step solution →
9. Q9
   Find the area of the shaded region in ​Fig. 11.9. The outer rectangle is 26 m by 12 m, and the ​unshaded inner region is ​a stadium shape (rectangle with two semicircular ​ends) ​leaving a 4 m border at top ​and bottom and ​a 3 m border at left and right.

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   Shaded area $=312-(64+4\pi )=248-4\pi \approx 235.43$ m${}^2$.

   Step-by-step solution →
10. Q10
    Find the area of the minor segment of ​a circle of ​radius ​14 cm, when the ​angle ​of the corresponding ​sector is $60^{\circ }$.
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    The area of the minor segment is $(308/3-49\sqrt{3})$ cm${}^2$, approximately 17.80 cm${}^2$.

    Step-by-step solution →
11. Q11
    Find ​the area of ​the ​shaded region in Fig. ​11.10, where arcs drawn with centres $A$, $B$, $C$ and $D$ intersect in pairs at mid-points $P$, $Q$, $R$ and $S$ of the ​sides $AB$, $BC$, $CD$ and $DA$, ​respectively of ​a square $ABCD$ (Use $\pi =3.14$).

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    The area of the shaded region is $144-113.04=30.96{\text{cm}}^2$.

    Step-by-step solution →
12. Q12
    In Fig. 11.11, 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 $\pi =3.14$.)

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    Shaded area $=39.25{\text{cm}}^2$.

    Step-by-step solution →
13. Q13
    In Fig. 11.12, arcs ​have ​been ​drawn with radii 14 ​cm each ​and with centres ​P, Q and R. Find the area of ​the shaded region.

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    Area of the shaded region $=308{\text{cm}}^2$.

    Step-by-step solution →
14. Q14
    A ​circular ​park is surrounded ​by a road 21 m wide. If the radius of ​the park ​is ​105 m, ​find the area of the road.
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    The area of the road is $15246$ m${}^2$.

    Step-by-step solution →
15. Q15
    In Fig. 11.13, ​arcs have been drawn of radius 21 cm ​each ​with vertices A, ​B, C and D of ​quadrilateral ABCD ​as centres. Find the ​area of the shaded region.

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    Area of the shaded region $=1386$ cm${}^2$.

    Step-by-step solution →
16. Q16
    A piece of wire 20 cm long ​is bent into the form of an ​arc ​of a circle subtending ​an ​angle of $60^{\circ }$ at ​its centre. ​Find the radius of the circle.
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    The radius of the circle is 210/11 cm, approximately 19.09 cm.

    Step-by-step solution →