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Areas Related to Circles

Short Answer Type

81. Two circles touch internally the sum of their areas is 116π cm² and distance between their centres is 6 cm. Find the radii of the circles.

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82. The inside perimeter of a running track, as shown in fig. is 340 m. The length of each straight portion is 60 m and the curved portions are semicircle. If the track is 7 m wide, find the area of the track. Also, find the outer perimeter of the track.

Length of inner curved portion
= [340 - (2 × 60) m
= (340 - 120) m = 220 m
Therefore, the length of each inner curved surface = 110 m.
Let radius be r, then
πr = 110 m
⇒r = 35 m
So, inner radius (OB = O'C)
= 35 m
and outer radius (OA = O'D) = (55 + 7)
= 42 m.
Hence, reqd. Area = (Area of 2 rectangles) + (Area of the circular rings)

$equals space open square brackets open parentheses 2 space straight x space 60 space straight x space 7 close parentheses space plus space 22 over 7 open square brackets open parentheses 42 close parentheses squared minus ? left parenthesis 35 right parenthesis squared close square brackets close square brackets straight m squared equals space open square brackets 840 plus 22 over 7 left parenthesis 42 space plus space 35 right parenthesis left parenthesis 42 space minus space 35 right parenthesis close square brackets straight m squared equals space left parenthesis 840 space plus space 1694 right parenthesis space straight m space equals space 2534 space straight m squared$

And, length of the outer boundary of the park

$equals space open parentheses 2 space straight x space 60 space plus space 2 space straight x space 22 over 7 straight x space 42 close parentheses space straight m equals space 384 space straight m.$

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83. The area of an equilateral triangle is

bold 49 square root of bold 3 bold space bold cm to the power of bold 2 bold.

Taking each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle as shown in fig. Find the area of the triangle not included in the circle.

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84. Find the area of the shaded region of Fig. 12.64, if the diameter of the circle with centre O is 28 cm and AQ =

1 fourth space AB.

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85. In Mr. Kumar's house there is a flower pot. The sum of radii of circular top and bottom of flower pot is 140 cm and the differences of their circumference is 88 cm. Find the diameter of the circular top and bottom.

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86. Abhishek Singh has a tractor. The sum of radii of two wheels of the tractor is 98 cm and the difference of their circumferences is 176 cm. Find the diameter of the wheel.

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87. The wheels of the car are 80 cm in diameter. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 80 cm/m.

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88.

A wheel of diameter 42 cm makes 240 rounds per minute. Find

(i) The total distance covered by the wheel in one minute.
(ii) The speed of the wheel in km/hr.)

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89. A square of side 4 cm is inscribed in a circle. Find the area enclosed between the circle and the square.

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90. A circular grassy land has perimeter of 660 m. A plot in the shape of a square having its vertices on the circumference of the field is marked in the field. Calculate the area of the square field.

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