Questions on mensuration ( circles)

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 circumferences of the two circles.

Solution: Circumference of first circle

= 2 πr = 2π x 19 = 38π cm

Circumference of second circle = 18π cm

Or, 2πr = 56π

Or, 2r = 56

Or, r = 28 cm

Circumference of the largest circle; as per question

= 38π + 18π = 56π cm

 

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

Answer:Area of first circle = πr2

= π82 = 64π sq cm

Area of second circle = π62 = 36π sq cm

As per question; area of the largest circle = 64π + 36π

= 100π sq cm

Or, πr2 = 100π

Or, r2 = 100

Or, r = 10 cm

 

3. 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?

Solution: Distance covered in 10 minutes = (66/60) x 10 = 11 km

Circumference = πd = 80π

[latex]\frac{22}{7}\times80[/latex]

[latex]\frac{22}{7}\times80\times\frac{1}{1000\times100}[/latex]

 

Number of revolutions = [latex]11\times1000\times100\times\frac{7}{22\times80}[latex] = 4375

4. Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

(A) 2 units (B) π units (C) 4 units (D) 7 units

Solution: (A) 2 units

2(pi) r = Pi(r)^2

r = 2

 

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

Solution: The minute hand makes an angle of 360o in 60 minutes.

Hence, angle made in 5 minutes = 30o

Area of sector = [latex]\frac{\theta}{360}\times\pi r^{2}[/latex]

= [latex]\frac{\theta}{360}\times\frac{22}{7} 14^{2}[/latex]

= 51.33 sq cm

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