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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°.

Here, we have

r = 6 cm and $straight theta$ = 60\
We know what that,

Area of sector = $pi tau to the power of italic 2 italic cross times theta over italic 360$

$equals space space space open parentheses 22 over 7 cross times 6 cross times 6 60 over 360 close parentheses space cm squared$
$space equals space 132 over 7 space cm cubed space equals space 18.86 space cm squared$