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

\frac{22}{7}\times80 \frac{22}{7}\times80\times\frac{1}{1000\times100}

 

Number of revolutions =

\frac{\theta}{360}\times\frac{22}{7} 14^{2}

= 51.33 sq cm

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