Chapter 12 Areas Related to Circles Ex 12.1

Chapter 12 Areas Related to Circles Ex 12.1

Question 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:
Given: radius of 1^st circle (R₁) = 19 cm
∴ Circumference of 1^st circle = 2πR₁ = 2π(19) cm
Radius of 2^nd circle (R₂) = 9 cm
∴ Circumference of 2^nd circle = 2πR₂ = 2π(9) cm
Let radius of 3^rd circle be R₃
Circumference of 3^rd circle = 2πR₃
According to question,
2πR₁ + 2πR₂ = 2πR₃
⇒ 2π(R₁ + R₂) = 2πR₃
⇒ R₁ + R₂ = R₃
⇒ 19 + 9 = R₃
⇒ R₃ = 28 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.
Solution:
Given: radius of 1^st circle (R₁) = 8 cm
Area of 1^st circle = πR₁² = π(8)²cm²
Radius of 2^nd circle (R₂) = 6 cm
Area of 2^nd circle = πR₂² = π(6)² cm²
Let radius of 3^rd circle be R₃
Area of 3^rd circle = πR₃²
According to question,

Question 3.
The figure depicts an archery target marked with its five scoring regions 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.

Question 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?

Question 5.
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) n units
(c) 4 units
(d) 7 units
Solution:
Let radius of the circle = r units
Perimeter of the circle = 2πr
Area of the circle = πr²
According to question,
Perimeter of the circle = Area of the circle
⇒ 2πr = πr²
⇒ r = 2 units
Hence, option (a) is correct.