# PSEB Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.1

PSEB Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.1

## PSEB 10th Class Maths Solutions 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:

Radius of first circle (r_{1}) = 19 cm

Radius of second circle (r_{2}) = 9 cm

Let radius of third circle be R cm

According to condition

circumference of first circle + circumference of second circle = circumference of third circle

2πr_{1} + 2πr_{2} = 2πR

2π (r_{1} + r_{2}] = 2πR

19 + 9 = R

∴ R = 28

∴ Radius of third circle (R) = 28 cm.

Question 2.

The Radii of two circles are 8 cm and 6 cm respectively. Find radius of circle which is having area equal to sum of the area of two circles.

Solution:

Radius of first circle (r_{1}) = 8 cm

Radius of second circle (r_{2}) = 6 cm

Let radius of third circle be R cm

According to question

Area of third circle = Area of first circle + Area of second circle

πR^{2} = πr_{1}^{2} + πr_{2}^{2}

πR^{2} = π[r_{1}^{2} + r_{2}^{2}]

R^{2} = (8)^{2} + (6)^{2}

R = √64+36 = √100

R = 10 cm

∴ Radius of required circle (R) = 10 cm.

Question 3.

Fig. depicts an archery target marLed with its five scoring areas from the centre ‘utwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score ¡s 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

Hence, area of gold ring; red ring; blue ring : black ring; white ring are 3465 cm^{2} ; 1039.5 cm^{2}; 1732.5 cm^{2}; 24255 cm^{2} ; 3118.5 cm^{2} respectively.

Question 4.

The wheels of a ca are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a spel of 66 km per hour?

Solution:

Question 5.

Tick the correct answer in the following and justify your choice : If the perimeter and area of a clrde are numerically equal, then the radius of the circle Is

(A) 2 units

(B) π units

(C) 4 units

(D) n units

Solution:

Perimeter of circle = Area of circle

2πR = πR^{2}

2R = R^{2}

⇒ R = 2

∴ Correct option A is (R) = 2 unit.

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