CBSE students can refer to NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Ex 11.3 Textbook Questions and Answers are provided by experts in order to help students secure good marks in exams.

## Class 7 Maths NCERT Solutions Chapter 11 Perimeter and Area Ex 11.3

**Question 1.**

Find the circumference of the circles with the following radius : ( Take π \(\frac { 22 }{ 7 } \))

**(a)** 14 cm

**(b)** 28 mm

**(c)** 21 cm

**Solution:
**

**Question 2.**

Find the area of the following circles, given that :

**(a)** radius = 14 mm (Take π = \(\frac { 22 }{ 7 } \))

**(b)** diameter = 49 m

**(c)** radius = 5cm

**Solution:
**

**Question 3.**

If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet (Take π = \(\frac { 22 }{ 7 } \))

**Solution:
**

**Question 4.**

A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase if he makes 2 rounds offence. Also find the cost of the rope, if it costs ₹ 4 per metre (Take π = \(\frac { 22 }{ 7 } \))

**Solution:
**

**Question 5.**

From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Take π = 3.14)

**Solution:**

Radius of outer circle (R) = 4 cm

Area of the outer circle = πR2

= 3.14 (4)^{2} cm^{2}

= 3.14 × 16 cm^{2}

= 50.24 cm^{2}.

Radius of inner circle (r) = 3 cm

∴ Area of the inner circle = πr^{2}

= 3.14 × (3)^{2} cm^{2}

= 28.26 cm^{2}

∴ Area of the remaining sheet = Area of the outer circle – Area of the inner circle

= 50.24 cm^{2} – 28.26 cm^{2}

= 21.98 cm^{2}.

**Question 6.**

Saima wants to put lace on the edge of a circular table cover of a diameter of 1.5 m. Find the length of the lace required and also its cost if one meter of the lace costs ₹ 15. (Take π = 3.14)

**Solution:
**

**Question 7.**

Find the perimeter of the adjoining figure, which is a semicircle including its diameter.

**Solution:
**

**Question 8.**

Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is ₹ 15/m^{2} (Take π = 3.14)

**Solution:
**

**Question 9.**

Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also, find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle of the square? (Take π = \(\frac { 22 }{ 7 } \))

**Solution:
**

**Question 10.**

From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed (as shown in the adjoining figure). Find the area of the remaining sheet (Take π = \(\frac { 22 }{ 7 } \))

**Solution:
**

**Question 11.**

A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the leftover aluminium sheet? (Take π = 3.14)

**Solution:**

Area of the square aluminium sheet = (6)^{2} cm^{2} = 36 cm^{2}

Area of the circle cut out from the sheet = (3.14 × 2 × 2) cm^{2} = 12.56 cm^{2}

Area of the sheet left over = (36 – 12.56) cm^{2} = 23.44 cm^{2}

**Question 12.**

The circumference of a circle is 31.4 cm. Find the radius and the area of the circle? (Take π = 3.14)

**Solution:
**

**Question 13.**

A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (π = 3.14)

**Solution:
**

**Question 14.**

A circular flower garden has an area of 314 m^{2}. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden? (Take π = 3.14)

**Solution:**

The radius of the area covered by the sprinkler at the centre of the garden (r) = 12 cm

∴ Area covered by the sprinkler at the centre of the garden = πr^{2
}= 3.14(12)^{2} m^{2}

= 452.16 m^{2} (> 314 m^{2})

Hence, the sprinkler will water the entire garden.

**Question 15.**

Find the circumference of the inner and the outer circles, shown in the adjoining figure. (Take π = 3.14)

**Solution:
**

**Question 16.**

How many times a wheel of radius 28 cm must rotate to go 352 m? (Take π = \(\frac { 22 }{ 7 } \))

**Solution:
**

**Question 17.**

The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour? (Take π = 3.14)

**Solution:**

Length of the minute hand of the circular clock = 15 cm

⇒ Radius of the circular clock (r) = 15 cm

∴ Circumference of the circular clock

= 2πr = 2 × 3.14 × 15 cm = 94.2 cm

⇒ Length moved by the tip of the minute hand in 1 hour = 94.2 cm

[As the minute hand makes one complete revolution round the clock in 1 hour].