Students can Download Class 10 Maths Chapter 5 Areas Related to Circles Ex 5.1 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 10 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.

## Karnataka State Syllabus Class 10 Maths Chapter 5 Areas Related to Circles Ex 5.1

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:

Radius of 1st Circle, r_{1} = 19 cm.

Circumference of 1st circle, C_{1} = 2πr_{1}

\(=2 \times \frac{22}{7} \times 19\)

Radius of 2nd circle, r_{2} = 9 cm.

Circumference of 2nd circle, C_{2} = 2πr_{2}

\(=2 \times \frac{22}{7} \times 9\)

Sum of the circumferences of the two circles

\(=2 \times \frac{22}{7} \times 19+2 \times \frac{22}{7} \times 9\)

\(C_{3}=2 \times \frac{22}{7}(19+9)\)

\(=2 \times \frac{22}{7} \times 28\)

= 2 × 22 × 4

∴ C_{3} = 176 cm.

Circumference of 3rd circle, C_{3} = 176 cm. then, r_{3}=?

2πr_{3} = C_{3}

\(2 \times \frac{22}{7} \times r_{3}=176\)

\(r_{3}=176 \times \frac{7}{22} \times \frac{1}{2}\)

∴ r_{3} = 28 cm

Question 2.

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having an area equal to the sum of the areas of the two circles.

Answer:

Radius of 1st Circle, r_{1} = 8 cm.

Area of 1st Circle, A_{1} = π r_{1}^{2}

\(=\frac{22}{7} \times(8)^{2}\)

\(A_{1}=\frac{22}{7} \times 64\)

Radius of 2nd Circle, r_{2} = 6 cm.

Area of 2nd Circle, A_{2} = π r_{2}^{2}

\(=\frac{22}{7} \times(6)^{2}\)

\(A_{2}=\frac{22}{7} \times 36\)

Total area of two circles =

Question 3.

The figure given 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 the 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:

i) The diameter of the region representing Gold Score: 21

d = 21 cm. ∴ Radius, \(r=\frac{21}{2} \mathrm{cm}\)

∴ Area of the region representing Gold score = πr^{2}

A = 346.5 sq. cm.

ii) Radius of the region representing Gold score and Red score:

r = 10.5 + 10.5 = 21 cm.

∴ Area of the region representing Red score: Area of the region representing Gold and Red Score – Area of the region representing Gold score = πr^{2} – π(r/2)^{2}

∴ A = 1039.5 sq.cm.

iii) Total radii of the region representing Gold, Red and Blue region :

r =10.5 + 10.5 + 10.5 = 31.5 cm

\(=\frac{63}{2} \mathrm{cm}\)

∴ Area of the region representing Blue region:

[ Area of the region representing Gold, Red and Blue regions ] – Area of the region representing Gold and Red region

∴ A = πr^{2} – πr^{2}

iv) Similarly, to find Area of the region representing Black region :

∴ A = πr^{2} – πr^{2}

∴ A = 2425.5 sq. cm.

v) Area of the region representing white:

∴ A = πr^{2} – πr^{2}

∴ A = 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 traveling at a speed of 66 km per hour?

Answer:

Diameter of the Wheel of the car = 80 cm.

Radius of the wheel = 40 cm.

Circumference of the Wheel = 2πr

\(=2 \times \frac{22}{7} \times 40\)

\(=\frac{44 \times 40}{7}\)

= 251.4 cm

Speed of the car = 66 km/hr.

\(=\frac{66 \times 100000}{60} \mathrm{cm} . / \mathrm{min}\)

= 110000 cm/min.

Distance travelled by car in 10 minutes

= 110000 × 10

= 1100000 cm.

Let the number of revolutions of the wheel be ’n’, then

n × 251.4= 1100000

\(\therefore \mathrm{n}=\frac{1100000}{251.4}\)

n = 4375

∴ Car can complete 4,375 revolutions in 10 minutes.

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) n units

C) 4 units

D) 7 units

Answer:

A) 2 units

Circumference of a circle = Area of the circle.

2πr = πr^{2}

2 × π × r = π × r × r

∴ 2 = r

∴ r = 2 units.