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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

We have,
r = Radius of the region representing Gold score = 10.5 cm
∴ r₁ = Radius of the region representing Gold and Red scoring areas = (10.5 + 10.5) cm = 21 cm = 2r cm
r₂ = Radius of the region representing Gold, Red and Blue scoring areas = (21 + 10.5) cm = 31.5 cm = 3r cm
r₃ = Radius of the region representing Gold, Red, Blue and Black scoring areas = (31.5 + 10.5) cm = 42 cm = 4r cm
r₄ = Radius of the region representing Gold, Red, Blue, Black and white scoring areas = (42 + 10.5) cm = 52.5 cm = 5r cm
Now, A, = Area of the region representing Gold scoring area

equals space πr space equals space 22 over 7 straight x left parenthesis 10.5 right parenthesis squared equals 22 over 7 straight x 10.5 space cross times space 10.5

= 22 × 1.5 × 10.5 = 346.5 cm²A₂ = Area of the region representing Red scorring area
= π (2r)² - πr² = 3πr² = 3A₁= 3 × 346.5 cm² = 1039.5 cm²A₃ = Area of the region representing Blue scoring area
= π(3r)² - π(2r)² = 9πr² - 4πr²= 5πr² = 5A₁ = 5 × 346.5 cm²= 1732.5 cm²A₄ = Area of the region representing black scoring area
= π(4πr)² - π(3r)² = 7πr² = 7A₁=7 × 346.5 cm² = 2425.5 cm²A₁ = Area of the region representing white scoring area
= π(5r)² - π(4r)² - 9πr² = 9 A₁= 9 × 346.5 cm² = 3118.5 cm²

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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.

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A chord of circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding :

(i) Minor segment
(ii) Major sector.

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10.

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find :

(i)    the length of the arc
(ii)    area of the sector formed by the arc
(iii)    area of the segment formed by the corresponding chord.

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