NCERT Solutions For Class 10 Math Chapter – 12 Exercise – 12.1
The NCERT Solutions for Class 10 Maths Chapter 12 Area related to the circle are undoubtedly an essential study materials for the students studying in CBSE Class 10 NCERT Solutions provided here along with the downnloads PDF can help the students prepare effectively for their first term exams The chapter is a continuation of what was taught in chapter probability in Class 9 and further explains the different concept related to it.
Q1. The radii of two circle are 19 cm and 9 cm respectively. Find the radius of the circle has which has circumference equal to the the sum of the circumference of the two circles.
Solution:-
Circumference of the circle with radius 19 cm = 2∏r = 2∏ x 19 = 38∏ cm.
Circumference of the circle with radius 9 cm = 2∏r = 2∏ x 9 = 18∏ cm.
Sum of the circumference of two circles = 38∏ + 18∏ = 56∏ cm.
Circumference of the third circle = 2∏r = 56∏r.
2∏r = 56∏ cm
R = 28 cm
The radius of the circle which has circumference equal to the sum of the circumferences of the two circles is 28 cm.
Q2. 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:-
Area of the circle with radius 8 cm = ∏ x 82 = 64∏ cm2
Area of the circle with radius 6 cm = ∏ x 62 = 36∏ cm2.
Sum of the area of two circles = 64∏ cm2 + 36∏ cm2 = 100∏ cm2
Area of the third circle = ∏r2 = 100∏ cm2
∏r2 = 100∏ cm2
R = 10 cm
Q3. Fig 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold , Blue , Red Black and White. The diameter of the region representing Gold score is 21 cm and each of the other band is 10.5 cm wide. Find the area of each of the five scoring regions.
Solution:-
Area of gold region = ∏r21 = ∏(10.5)2 = 346.5 cm2
Area of red region = Area of second circle – Area of first circle
= 1386 – 346.5 cm2
= 1039.5 cm2
Area of blue region = Area of third circle – Area of second circle = 3118 – 1386 = 1732 cm2
Area of black region = Area of fourth circle – Area of third circle
= 5544 – 3118.5
= 2425.5 cm2
Area of white region = Area of fifth circle – Area of fourth circle
= 8662.5 – 5544
= 3118.5 cm2
Q4. 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 travelled by car in 10 minutes = (66 x 1000 x 100 x 10)/60 = 1100000 cm/s
No of revolutions = Distance travelled by car/ Circumference of wheels
= 1100000/80 ∏ = 4375
4375 complete revolutions does each wheel make in 10 minutes.
Q5. Tick the correct answer n the following and justify your choice If the perimeter ad the area of a circle are numerically equal , then the radius of the circle is
- 2 units (b) ∏units © 4 units (d) 7 units
Solution:-
- (A) Is correct option
- Circumference of the circle with radius 19 cm = 2