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Class 10 Maths NCERT Solutions for Circle



In this page we have NCERT book Solutions for Class 10th Maths:Circle for EXERCISE 1 . Hope you like them and do not forget to like , social share and comment at the end of the page.

1) The radii of the two circles are 19cm 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 1:

According to the question

Circumference of Ist circle =  2π(19)  =38 π cm

Circumference of 2nd  circle =  2π(9)  =18 π cm

Let r be the radius of the new circle

Circumference of New  circle =  2π(r)  =2 πr cm

Now

2πr=38π+18π

Or r =28 cm

 

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 2:

According to the question

Area of Ist circle =πr2=π(64)=64π

Area of 2nd circle =πr2=π(36)=36π

Let  r the radius of new circle

Area of New circle=πr2

Now as per question

πr2= 64 π+36 π

r=10cm

 

3. The below 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.


Solution:

Diameter of Gold Circle is given as =21 cm

Radius of Gold circle=21/2=10.5 cm

Area of Gold region is given by

= πr2= (22/7) (10.5)2= 346.5 cm 2

Now since each band  is 10.5 cm wide

Radius of red ring= 10.5+ 10.5=21 cm

Now Radius of Red ring is given as

= π(21)2  - π(10.5)2  = 1386-346.5=1039.5 cm2

Radius of Blue ring =21 +10.5=31.5 cm

Now Radius of Blue ring is given as

= π(31.5)2  - π(21)2  = 3118.5-1386=1732.5 cm2

 

Radius of Black ring =31.5 +10.5=42 cm

Now Radius of Black ering is given as

= π(42)2  - π(31.5)2  = 5544-3118.5=2425.5 cm2

Radius of White ring =42 +10.5=52.5 cm

Now Radius of Black ering is given as

= π(52.5)2  - π(42)2  = 8662.5-5544=3118.5 cm2

 

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?

Solution:

Diameter of wheel is given as =80 cm

So radius of the wheel=40 cm

So circumference of wheel =2πr= 2(22/7)(40)= (1760/7)cm

So in 1 revolution, Car travels the distance  (1760/7)cm

Now Speed of the Car= 66Km/h

=(66X1000)/60   meter/minute

=1100 meter/minute

=110000 cm/minute

This mean in simple term

Distance travelled in 1 min =  110000 cm

Distance travelled in 10 min=1100000  cm

So Total number of revolutions =( 1100000)/(1760/7)

 =4375

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

Solution:

Area of Circle  = πr2

Circumference of Circle =2πr

According to the question

πr2 = 2πr

r=2 units

 

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