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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.

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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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6. Find the area of a sector of a circle with radius 6 cm and of angle 60°.

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7. Find the area of a quadrant of a circle whose circumference is 22 cm.

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8. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

The angle described by the minute hand in 1 minute = 66°
∴ The angle described by 1 minute hand in 5 minutes = 30°
i.e. ө = 30° and r = 14 cm
Now, area swept by the minute hand

$equals space πr squared cross times straight theta over 360 equals space open parentheses 22 over 7 cross times 14 cross times 14 cross times 30 over 360 close parentheses space space cm squared equals space 51.3 space space cm squared$