Table of Contents

Toggle## Class 7, Maths, Chapter 11, Exercise 11.3 Solutions

**Q.1. Find the circumference of the circles with the following radius: (Take π =22/7 )**

**(a) 14 cm **

**(b) 28 mm **

**(c) 21 cm**

**Q.2. Find the area of the following circles, given that:**

**(a) radius = 14 mm (Take π =22/7 ) **

**(b) diameter = 49 m**

**(c) radius = 5 cm**

**Q.3. If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet. (Take π = 22/7)**

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

**Q.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)**

**Q.6. Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs ****₹****15. (Take π = 3.14)**

**Q.7. Find the perimeter of the adjoining figure, which is a semicircle including its diameter.**

**Q.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)**

**Q.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 or the square? (Take π = 22/7)**

**Q.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 1cm are removed. (as shown in the adjoining figure). Find the area of the remaining sheet. (****Take π = 22/7)**

**Q.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 left-over aluminium sheet? (Take π = 3.14)**

**Q.12. The circumference of a circle is 31.4 cm. Find the radius and the area of the circle? (Take π = 3.14)**

**Ans: **

Circumference of a circle = 31.4 cm

we know that,

**Circumference of a circle = 2πr**

⟹ 31.4 = 2 x 3.14 x r

⟹ 31.4 = 6.28 x r

⟹ $\frac{31.4}{6.28}=r$

⟹ **r = 5 cm**

Then, Area of the circle

= πr^{2}

= 3.14 x (5)^{2}

= 3.14 x 5 x 5

**= 78.5 cm ^{2}**

Hence, the radius and the area of the circle area 5 cm and 78.5 cm^{2} respectively.

**Q.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)**

**Q.14. A circular flower garden has an area of 314 m2. 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)**

**Ans: **

Area of the circular flower garden = **314 m ^{2}. [Given]**

∵ Area of circular garden with radius 12 cm, covered by the **sprinkler = πr ^{2}**

= 3.14 x (12)^{2} [∵ r = 12 m]

= 3.14 x 12 x 12

= 3.14 x 144

**= 552.16 m ^{2}**

So, Area of circular garden covered by the **sprinkler = 552.13 m ^{2}**

Here,

clearly, we can say that, area of circular flower garden is smaller than area covered by sprinkler. Therefore, the sprinkler will water the entire garden.

**Q.15. Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14)**

**Ans: **

Radius of outer circle, R = 19 m

∴ Circumference of outer circle

= 2πR

= 2 x 3.14 x 19

= 119.32 m

Now radius of inner circle, (r)

r = radius of outer circle (R) – 10

r = R – 10

r = 19 – 10

= 9 m

∴ Circumference of inner circle

= 2πr

= 2 x 3.14 x 9

= 56.52 m

Therefore, the circumferences of inner and outer circles are 56.52 m and 119.32 m respectively.

**Q.16. How many times a wheel of radius 28 cm must rotate to go 352 m? (Take π = 22/7)**

**Q.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)**

**Ans:**

In 1 hour, minute hand completes one round means makes a circle.

∴ Radius of the circle, r = 15 cm

Then,

Distance travelled by the tip of minute hand in 1hour = circumference of the clock

Circumference of circular clock:

= 2πr

= 2 x 3.14 x 15

= 94.2 cm

Therefore, the tip of the minute hand moves 94.2 cm in 1 hour.

## NCERT Solutions For Class 7 Maths, Chapter 11, Perimeter and Area (All Exercises)

**Class 7, Maths, Chapter 11, Perimeter and Area **

**Class 7, Maths, Chapter 11, Perimeter and Area, Exercise 11.1**

**Class 7, Maths, Chapter 11, Perimeter and Area, Exercise 11.2**

**Class 7, Maths, Chapter 11, Perimeter and Area, Exercise 11.3** **← You are here**

**Class 7, Maths, Chapter 11, Perimeter and Area, Exercise 11.4**