Area of Circle

NCERT Exercise 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.

Answer: Circumference of first circle

`= 2 πr = 2π xx 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 `= πr^2`

`= π8^2 = 64π  sq  cm`

Area of second circle `= π6^2 = 36π  sq  cm`

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

`= 100π  sq  cm`

Or, `πr^2 = 100π`

Or, `r^2 = 100`

Or, `r = 10  cm`

Question: 3: Following figure 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.

Answer: Area of Gold Region `= πr^2`

`= π10.5^2 = 110.25^2 = 346.5  sq  cm`

Area of Red Region `= πr^2`

`= π21^2 - π10.5^2`

`= π(21^2 – 10.5^2)`

`= π(21 + 10.5)(21 – 10.5)`

`= π xx 31.5 xx 10.5 = 1039.5  sq  cm`

Area of Blue Region `= πr^2`

`= π(31.5^2 – 21^2) = 1732.5  sq  cm`

Area of Black Region `= πr^2`

`= π(42^2 – 31.5^2) = 2425.5  sq  cm`

Area of White Region `= πr^2`

`= π(52.5^2 – 42^2) = 3118.5  sq  cm`

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?

Answer: Distance covered in 10 minutes `= (66)/(60) xx 10 = 11  km`

Circumference `= πd = 80π`

`=(22)/(7)xx80 cm`

`=(22)/(7)xx80xx(1)/(1000xx100) km`

Number of revolutions

`=11xx1000xx100xx(7)/(22xx80)`

`=4375`

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) π units (C) 4 units (D) 7 units

Answer: (A) 2 units

Explanation:

`2πr=πr^2`
Or, `(πr^2)/( πr)=2`

Or, `r=2`