The document Solved Examples - Areas Related to Circles, CBSE, Class 10, Mathematics Class 10 Notes | EduRev is a part of Class 10 category.

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**Ex.1 Calculate the circumference and area of a circle of radius 5·6 cm.**

**Sol. **We have :

Circumference of the circle

Area of the circle

**Ex.2 The circumference of a circle is 123·2 cm. Calculate : (i) the radius of the circle in cm, (ii) the area of the circle, correct to nearest cm**

**Sol. **(i) Let the radius of the circle be r cm.

Then, its circumference = (2πr) cm.

**Ex.3 The area of a circle is 301·84 cm ^{2}. Calculate:**

**(i) the radius of the circle in cm.**

**(ii) the circumference of the circle, correct to nearest cm.**

**Sol.** (i) Let the radius of the circle be r cm.

Then, its area = πr^{2} cm^{2} = 301.84

= 61.6 cm.

Circumference of the circle, correct to nearest cm = 62 cm.

**Ex.4 The perimeter of a semi-circular protractor is 32·4 cm. Calculate :**

**(i) the radius of the protractor in cm,**

**(ii) the area of the protractor in cm ^{2}.**

**Sol.** (i) Let the radius of the protractor be r cm.

Radius of the protractor = 6.3 cm.

(ii) Area of the protractor

Area of the protractor = 62·37 cm^{2}.

**Ex.5 The area enclosed by the circumferences of two concentric circles is 346.5 cm ^{2}. If the circumference of the inner circle is 88 cm, calculate the radius of the outer circle.**

**Sol.** Let the radius of inner circle be r cm.

Then, its circumference = (2πr) cm.

Hence, the radius of the outer circle is 17·5 cm.

**Ex.6 Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centres is 14 cm. Determine the radii of the circles.**

**Sol. **Let the radii of the given circles be R cm and r cm respectively. As the circles touch externally, distance between their centres = (R + r) cm.

**Ex.7 Two circles touch internally. The sum of their areas is 116π sq. cm and the distance between their centres is 6 cm. Find the radii of the given circles.**

**Sol.** Let the radii of the given circles be R cm and r cm respectively. As the circles touch internally, distance between their centres = (R – r) cm.

**Ex.8 The wheel of a cart is making 5 revolutions per second. If the diameter of the wheel is 84 cm, find its speed in km/hr. Give your answer, correct to nearest km.**

**Sol. **Radius of the wheel = 42 cm.

Circumference of the wheel =

Distance moved by the wheel in 1 revolution = 264 cm.

Distance moved by the wheel in 5 revolutions = (264 × 5) cm = 1320 cm.

Distance moved by the wheel in 1 second = 1320 cm.

Distance moved by the wheel in 1 hour = (1320 × 60 × 60) cm.

Hence, the speed of the cart, correct to nearest km/hr is 48 km/hr.

**Ex.9 The diameter of the driving wheel of a bus is 140 cm. How many revolutions must the wheel make in order to keep a speed of 66 km/hr?**

**Sol.** Distance to be covered in 1 min.

Hence, the wheel must make 250 revolutions per minute.

**Ex.10 A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascends in 1 min. 28 seconds with a uniform speed of 1·1 m / sec, calculate the number of complete revolutions the wheel makes in raising the bucket.**

**Sol. **Time taken by bucket to ascend = 1 min. 28 sec. = 88 sec. Speed = 1.1 m/sec.

Length of the rope = Distance covered by bucket to ascend

= (1·1 × 88) m = (1·1 × 88 × 100) cm = 9680 cm.

Circumference of the wheel

Hence, the wheel makes 40 revolutions to raise the bucket.

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