Hell Fridens this blog we provide complete solution of CBSE Board 10th Math Solution of Chapter 12. Please goo through this blog and check NCERT Solutions for Class 10th Exercise 12, NCERT Solutions of Class 10th of Exercise 12.1. CBSE 10th Math Exercise 12.1, CBSE 10th Class Math Chapter 12.1 Complete Solutions is given here. For other chapter solutions please stay connect this blog. If you have any doubt of NCERT Book Questions Please write comment in comment section. we will provide you complete solution.
Q.1 The radii of two circles are 19 cm & 9 cm respectively. Calculate the radius of
the circle which has circumference equal to the sum of the circumferences of
the two circles.
Answer
Let the radius of third circle is R.
Then Circumference of
the circle of Radius is = 2πR
Circumference of the circle of radius 19 cm will be = 2π × 19 = 38π cm
And 9cm Radius circle
Circumference is = 2π × 9 = 18π cm
Sum of the circumference of these two circles is = 18 π + 38π = 56π cm
Then Circumference of
the third circle is = 2πR = 56π
⇒ 2πR = 56π cm
⇒ R = 28 cm Ans.
2. The radii of two
circles are 8 cm and 6 cm respectively. Calculate the radius of the circle
having area equal to the sum of the areas of the two circles.
Explanation
We assume that radius of third circle is R.
Area of circle is = πR2
Radius 8 cm circle’s Area = π × 82 = 64π cm2
Radius 6 cm Circle
Area is = π × 62 = 36π cm2
Sum of the area of two circles is = 36π cm2 + 64π cm2 = 100π cm2
⇒ πR2 = 100π cm2
⇒ R2 = 100 cm2
⇒ R = 10 cm Ans.
Radius of the new circle is 10 cm.
Q. 3. Fig. 12.3 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.
Explanation
Diameter of Gold circle or first circle is = 21 cm
Then Radius of first circle, r1 is = 21/2 cm = 10.5 cm
Each of other bands
is 10.5 cm wide,
Radius of Red or second circle, r2
= 10.5 cm + 10.5 cm = 21 cm
Radius of third or Blue circle, r3
= 21 cm + 10.5 cm = 31.5 cm
Radius of fourth or Black circle, r4
= 31.5 cm + 10.5 cm = 42 cm
Radius of fifth or white circle, r5 is = 42 cm + 10.5 cm = 52.5 cm
Area of gold region = π r12 = 22/7*(10.5)2=
346.5 cm2
Area of red region = Area of second circle – Area of first
circle = π r22 – 346.5 cm2
= π(21)2 –
346.5 cm2 = 1386 – 346.5 cm2 = 1039.5 cm2
Area of blue region = Area of third circle – Area of second
circle = π r32 – 1386 cm2
= π(31.5)2 – 1386 cm2 = 3118.5 –
1386 cm2 = 1732.5 cm2
Area of black region = Area of fourth circle – Area of third
circle = π r32 – 3118.5 cm2
= π(42)2 –
1386 cm2 = 5544 – 3118.5 cm2 = 2425.5 cm2
Area of white region = Area of fifth circle – Area of fourth
circle = π r42– 5544 cm2
= π(52.5)2
– 5544 cm2 = 8662.5 – 5544 cm2 = 3118.5 cm2
Q.4. The wheels of a car are of diameter is 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 /H?
Explanation
Diameter of the wheels = 80 cm
And the Circumference of wheels is = 2πr = 2r × π = 80 π cm
Then Distance
travelled by car in 10 minutes = (66 × 1000 × 100 × 10)/60 = 1100000 cm/s
Formula “No. of
revolutions = Distance travelled by car/Circumference of wheels”
= 1100000/80 π = (1100000 × 7)/(80×22) = 4375 Ans.
Q.5. Tick the correct answer in given below & 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
Let the radius of circle r.
Perimeter of the circle = 2πr
Area of the circle = π r2
A/q,
2πr = π r2
⇒ 2 = r
The radius of the circle is 2 units Then (A) is
correct.
No comments:
Post a Comment