NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To CirclesExercise 11.3
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles
Question. 1
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.
Answer:
33 cm
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Question. 2
In Fig. 11.5, a square of diagonal 8 cm is inscribed in a circle. Find the area of the shaded region (circle minus square).
Answer:
\(16\pi - 32\;\text{cm}^2\) (≈ 18.27 cm² if \(\pi=3.14\))
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Question. 3
Find the area of a sector of a circle of radius 28 cm and central angle \(45^\circ\).
Answer:
\(98\pi\;\text{cm}^2\) (≈ 307.88 cm²)
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Question. 4
The radius of a motorcycle wheel is 35 cm. How many revolutions per minute must it make to keep a speed of 66 km/h?
Answer:
500 rpm
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Question. 5
A cow is tied with a rope 14 m long at the corner of a rectangular field of dimensions 20 m × 16 m. Find the area it can graze.
Answer:
\(49\pi\;\text{m}^2\) (≈ 153.94 m²)
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Question. 6
Find the area of the flower bed with semicircular ends shown in Fig. 11.6. The overall length is 38 cm and the overall width is 10 cm.
Answer:
\(280 + 25\pi\;\text{cm}^2\) (≈ 358.50 cm²)
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Question. 7
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 \(\pi = 3.14\)).
Answer:
54.5 cm²
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Question. 8
Find the area of the shaded field shown in Fig. 11.8. (Top width 8 m, left height 6 m with a semicircular bulge, right height 4 m with a semicircular bulge.)
Answer:
\(32 + 6.5\pi\;\text{m}^2\) (≈ 52.42 m²)
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Question. 9
Find the area of the shaded region in Fig. 11.9 (outer rectangle 26 m × 12 m; inner 'stadium' has total length 20 m and width 4 m).
Answer:
\(248 - 4\pi\;\text{m}^2\) (≈ 235.43 m²)
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Question. 10
Find the area of the minor segment of a circle of radius 14 cm when the angle of the corresponding sector is \(60^\circ\).
Answer:
\(\dfrac{98\pi}{3} - 49\sqrt{3}\;\text{cm}^2\) (≈ 21.99 cm²)
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Question. 11
In Fig. 11.10 (square of side 12 cm), arcs with centres at \(A,B,C,D\) and radius 6 cm pass through the midpoints of adjacent sides, forming a central shaded region. Find the shaded area (use \(\pi=3.14\)).
Answer:
\(144 - 36\pi\;\text{cm}^2\;\approx 30.96\,\text{cm}^2\)
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Question. 12
In Fig. 11.11, an equilateral triangle \(ABC\) of side 10 cm has arcs centred at \(A,B,C\) that meet sides at their midpoints \(D,E,F\). Find the area of the shaded central region (use \(\pi=3.14\)).
Answer:
\(25\sqrt{3} - \dfrac{25\pi}{2}\;\text{cm}^2\) (≈ 3.04 cm²)
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Question. 13
In Fig. 11.12, arcs are drawn with radii 14 cm and with centres at the triangle’s vertices \(P, Q, R\). Find the area of the shaded regions near the vertices.
Answer:
\(98\pi\;\text{cm}^2\) (≈ 307.88 cm²)
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Question. 14
A circular park is surrounded by a road 21 m wide. If the park’s radius is 105 m, find the area of the road.
Answer:
\(4851\pi\;\text{m}^2\) (≈ 15{,}226.1 m²)
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Question. 16
A piece of wire 20 cm long is bent into an arc of a circle subtending an angle of \(60^\circ\) at the centre. Find the radius of the circle.
Answer:
\(\dfrac{60}{\pi}\;\text{cm}\) (≈ 19.10 cm)