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Areas Related to Circles

Short Answer Type

91. In an equilateral triangle of side 24cm, a circle is inscribed touching its sides. Find the area of the remaining portion of the triangle.

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92. A chord AB of a circle of radius 20 cm subtends a right angle at the centre. Find the area of the minor segment, the area of and the area of a major segment.

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93. The following diagram shows an equi-lateral triangle ABC. Circles are drawn with vertices of the triangle ABC as centres so that every circle touches the remaining two.

If the perimeter of the triangle is 84 cm, find.

(i) area of sector, inside the triangle of each circle.
(ii) area of the triangle ABC
(iii) Area of the circle not included in the circle.

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94. A drain cover is made from a square metal plate of side 40 cm by having 441 holes of diameter 1 cm each drilled in it. Find the area of the remaining square plate.

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95. A square heater tank has its sides equal to 40 m. There are four semicircular grassy plots all round it. Find the cost of turfing the plots at Rs. 1.25 per sq. m.

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96. Find the area of the region ABCDEFA shawn in the figure, given that ABDE is a square of side 10 cm. BCD is a semicircle with BD as diameter, EF = 8 cm, AF = 6 cm and ∠AFE = 90° (π = 3.14)

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97. Three horses are tethered with 7 cm long ropes at the three comers of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses. Also, find the area of the point which remains ungrazed.

Clearly, let
∠A = ө₁, ∠B = ө₂ ∠C = ө₃

We have,
r = 7 m,
a = 34 m, b = 42 m, c= 20 m
Now, area which can be grazed by the horses = Sum of the areas of three sectors with central angles ө₁, ө₂ and ө₃ each with radius (r) = 7 m

Now, we can find out area of the triangle by using Heron's formula.
Here, we have

Clearly, let∠A = ө1, ∠B = ө2 ∠C = ө3
We have,r = 7 m,a = 34

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98. The minute hand of a clock is 12 cm long. Find the area of the face of the clock described by minute hand in 35 minutes.

Fig. 12.58

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99. OAPB is a sector of a circle of radius 3.5 cm with the centre at O and ∠AOB = 120°. Find the length of OAPBO.

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100. A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel.

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