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Let the radius of the bigger circle be R cm. and radii of two smaller circles are r 1 and r 2 , then according to question. 2πR = 2πr 1 + 2πr 2 ⇒ 2πR = 2π (19) + 2π (9) ⇒ 2πR = 2π (19 + 9) ⇒ R = 28 Hence, radius of the circle be 28 cm.

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Areas Related to Circles

Short Answer Type

1. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumference of two circles.

Let the radius of the bigger circle be R cm. and radii of two smaller circles are r₁and r₂, then according to question.

2πR = 2πr₁ + 2πr₂⇒    2πR = 2π (19) + 2π (9)
⇒    2πR = 2π (19 + 9)
⇒    R = 28
Hence, radius of the circle be 28 cm.

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2. The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.

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Long Answer Type

3. Fig. 12.3, depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

Fig. 12.3

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Short Answer Type

4. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

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Tick the correct answer in the following: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(A) 2 units (D) π units
(C) 4 units (D) 7 units.

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