NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To CirclesExercise 11.4
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles
Question. 1
The area of a circular playground is \(22176\,\text{m}^2\). Find the cost of fencing this ground at the rate of Rs 50 per metre.
Answer:
Rs 26,400
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Question. 2
Diameters of the front and rear wheels of a tractor are 80 cm and 2 m, respectively. How many revolutions will the rear wheel make in the distance in which the front wheel makes 1400 revolutions?
Answer:
560 revolutions
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Question. 3
Sides of a triangular field are 15 m, 16 m and 17 m. From the three corners, a cow, a buffalo and a horse are tied with ropes of length 7 m each to graze the field. Find the area of the field which cannot be grazed by the three animals.
Answer:
\(24\sqrt{21} - \dfrac{49\pi}{2}\,\text{m}^2 \;\approx\; 33.0\,\text{m}^2\)
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Question. 4
Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of \(60^\circ\) (Use \(\pi=3.14\)).
Answer:
\(\approx 13.01\,\text{cm}^2\)
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Question. 5
A circular pond is 17.5 m in diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs 25 per m2.
Answer:
Cost = \(975\pi\) Rs \(\approx\) Rs 3,064
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Question. 6
In the trapezium ABCD, \(AB\parallel DC\), \(AB=18\,\text{cm}\), \(DC=32\,\text{cm}\) and the distance between them is \(14\,\text{cm}\). Arcs of equal radii 7 cm with centres A, B, C and D are drawn as in the figure. Find the area of the shaded region.
Answer:
\(350 - 49\pi\,\text{cm}^2 \;\approx\; 196.1\,\text{cm}^2\)
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Question. 7
Three circles each of radius 3.5 cm are drawn so that each touches the other two. Find the area enclosed between these circles.
Answer:
\(\dfrac{49\sqrt{3}}{4} - \dfrac{49\pi}{8}\,\text{cm}^2 \;\approx\; 1.97\,\text{cm}^2\)
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Question. 8
Find the area of the sector of a circle of radius 5 cm if the corresponding arc length is 3.5 cm.
Answer:
\(8.75\,\text{cm}^2\)
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Question. 9
Four circular cardboard pieces of radius 7 cm are placed on a paper so that each piece touches the other two. Find the area of the portion enclosed between these pieces.
Answer:
\(196 - 49\pi\,\text{cm}^2 \;\approx\; 42.06\,\text{cm}^2\)
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Question. 10
On a square cardboard sheet of area \(784\,\text{cm}^2\), four congruent circular plates of maximum size are placed such that each plate touches two others and each side of the square is tangent to two plates. Find the area of the square sheet not covered by the plates.
Answer:
\(784 - 196\pi\,\text{cm}^2 \;\approx\; 168.25\,\text{cm}^2\)
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Question. 11
The floor of a room is \(5\,\text{m}\times 4\,\text{m}\) and it is covered with circular tiles of diameter 50 cm laid in a rectangular grid as shown. Find the area of the floor that remains uncovered with tiles.
Answer:
\(200000 - 50000\pi\,\text{cm}^2 \;\approx\; 42{,}920\,\text{cm}^2 = 4.292\,\text{m}^2\)
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Question. 12
All the vertices of a rhombus lie on a circle. If the area of the circle is \(1256\,\text{cm}^2\) (use \(\pi=3.14\)), find the area of the rhombus.
Answer:
\(800\,\text{cm}^2\)
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Question. 13
An archery target has three regions formed by three concentric circles whose diameters are in the ratio \(1:2:3\). Find the ratio of the areas of the three regions.
Answer:
\(1 : 3 : 5\)
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Question. 14
The length of the minute hand of a clock is 5 cm. Find the area swept by it from 6:05 a.m. to 6:40 a.m.
Answer:
\(\dfrac{175}{12}\,\pi\,\text{cm}^2 \;\approx\; 45.8\,\text{cm}^2\)
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Question. 15
The area of a sector of central angle \(200^\circ\) of a circle is \(770\,\text{cm}^2\). Find the length of the corresponding arc.
Answer:
\(\dfrac{70}{3}\,\pi\,\text{cm} \;\approx\; 73.3\,\text{cm}\)
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Question. 16
The central angles of two sectors of circles of radii 7 cm and 21 cm are respectively \(120^\circ\) and \(40^\circ\). Find the areas and arc lengths of the two sectors. What do you observe?
Answer:
Areas: \(\dfrac{49\pi}{3}\,\text{cm}^2\) and \(49\pi\,\text{cm}^2\). Arc lengths: both \(\dfrac{14\pi}{3}\,\text{cm}\).
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Question. 17
Find the area of the shaded region shown in Fig. 11.20.
Answer:
\(196 - 18\pi\,\text{cm}^2 \;\approx\; 139.5\,\text{cm}^2\)
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Question. 18
A circular wheel of area \(1.54\,\text{m}^2\) rolls a distance of \(176\,\text{m}\). Find the number of revolutions made by the wheel.
Answer:
40 revolutions
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Question. 19
A chord of length 5 cm subtends an angle of \(90^\circ\) at the centre. Find the difference between the areas of the two segments formed by the chord.
Answer:
\(\dfrac{25}{4}(\pi+2)\,\text{cm}^2 \;\approx\; 32.14\,\text{cm}^2\)
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Question. 20
Find the difference of the areas of a sector of angle \(120^\circ\) and its corresponding major sector of a circle of radius 21 cm.
Answer:
\(147\pi\,\text{cm}^2 \;\approx\; 461.8\,\text{cm}^2\)