The document NCERT Solutions(Part - 2) - Perimeter and Area Class 7 Notes | EduRev is a part of the Class 7 Course Mathematics (Maths) Class 7.

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**EXERCISE 11.3**

**Q.1. Find the circumference of the circles with the following radius:****(a) 14 cm**

**(b) 28 mm **

**(c) 21 cm **

**Solution.**

(a) A circumference of the circle

(b) A circumference of the circle

(c) A circumference of the circle** ****Q.2. ****Find the area of the following circles, given that: ****(a) radius = 14 mm **

**(b) diameter = 49 m **

**(c) radius = 5 cm **

**Solution.**

**Q.3. ****If the circumference of a circular sheet is 154 m, find its radius. Also, find the area of the sheet. **

**Solution.**** **

Circumference of the circular sheet = 154 m** **

â‡’ 2Ï€r = 154 m

â‡’ r = 154/2Ï€

â‡’

Now, Area of circular sheet =Ï€r^{2}

= 22 x 3.5 x 24.5 = 1886.5 m^{2}

Thus, the radius and area of circular sheet are **24.5 m** and **1886.5 m**^{2} respectively.**Q.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 of a fence. Also, find the costs of the rope, if it cost Rs 4 per meter. **

**Solution.**

Diameter of the circular garden = 21 m

âˆ´ Radius of the circular garden = 21/2 m

Now, Circumference of a circular garden

= 22 x 3 = 66 m

The gardener makes 2 rounds of a fence so the total length of the rope of fencing

= 2 x 2Ï€r

= 2 x 66 = **132 m**

Since, the cost of 1 meter rope = Rs 4

Therefore, Cost of 132 meter rope = 4 x 132 = **Rs 528****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. **

**Solution.**

Radius of circular sheet (R) = 4 cm and radius of removed circle (r) = 3 cm

Area of the remaining sheet = Area of a circular sheet - Area of removed circle

Thus, the area of the remaining sheet is **21.98 cm**^{2}.**Q.6. ****Saima wants to put 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 Rs 15. **

**Solution.**

Diameter of the circular table cover = 1.5 m

âˆ´ Radius of the circular table cover = 1.5/2 m

Circumference of circular table cover = 2Ï€r= 4.71 m

Therefore, the length of required lace is **4.71 m**.

Now the cost of 1 m lace = Rs 15

Then the cost of 4.71 m lace = 15 x 4.71 = Rs 70.65

Hence, the cost of 4.71 m lace is **Rs 70.65**.**Q.7. ****Find the perimeter of the adjoining figure, which is a semicircle including its diameter. **

**Solution.**

Diameter = 10 cm

Radius = 10/2 = 5 cm

According to question,**Perimeter of figure = Circumference of semicircle + diameter**

Thus, the perimeter of the given figure is** ****25.71 cm.****Q.8. ****Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is Rs 15/m ^{2}. (Take Ï€ = 3.14)**

**Solution.**

Diameter of the circular table top = 1.6 m

Radius of the circular table top = 1.6/2 = 0.8 m

Area of circular table top = Ï€r^{2} = 3.14 x 0.8 x 0.8 = 2.0096 m^{2}

Now, the cost of polishing 1 m^{2} = Rs 15

Then cost of polishing 2.0096 m^{2} = 15 x 2.0096 = Rs 30.14 (approx.)

Thus, The cost of polishing a circular table top is Rs 30.14 (approx.)**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? **

**Solution.**

Total length of the wire = 44 cm

âˆ´ The circumference of the circle = 2Ï€r = 44 cm

Now Area of the circle = Ï€r^{2}

Now the wire is converted into the square.

The perimeter of square = 44 cm

Now, area of square = side x side = 11 x 11 = **121 cm**^{2}

Therefore, on comparing, the area of the circle is greater than that of a square, so the circle encloses more area.**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 1 cm are removed (as shown in the adjoining figure). Find the area of the remaining sheet. **

**Solution.**

Radius of circular sheet (R) = 14 cm and Radius of smaller circle (r) = 3.5 cm

Length of rectangle (l) = 3 cm and breadth of rectangle (b) = 1 cm

According to question,

Area of remaining sheet = Area of circular sheet- (Area of two smaller circle + Area of rectangle)

Therefore, the area of the remaining sheet is **536 cm ^{2}.**

**Solution.**

Radius of circle = 2 cm and side of aluminium square sheet = 6 cm

According to question,

Area of aluminum sheet left = Total area of aluminum sheet - Area of circle

= side x side - Ï€r^{2}

Therefore, the area of the aluminum sheet left is **23.44 cm ^{2}.**

**Q.12. ****The circumference of a circle is 31.4 cm. Find the radius and the area of the circle. **

**Solution.**

The circumference of the circle = 31.4 cm

Then area of the circle = Ï€r^{2} = 3.14 x 5 x 5

= 78.5 cm^{2}

Therefore, the radius and the area of the circle are **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? **

**Solution.**

Diameter of the circular flower bed = 66 m

âˆ´ Radius of circular flower bed (r) = 66/2 = 33 m

âˆ´ Radius of circular flower bed with 4 m wide path (R) = 33 + 4 = 37 m

According to question,

Area of path = Area of bigger circle - Area of smaller circle

= 3.14 x 70 x 4

= 879.20 m^{2}

Therefore, the area of the path is **879.20 m ^{2}.**

**Solution.**

Circular area covered by the sprinkler = Ï€r^{2}

= 3.14 x 12 x 12

= 3.14 x 144

= 452.16 m^{2}

Area of the circular flower garden = 314 m^{2}

As Area of the circular flower garden is smaller than area with a 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. **

**Solution.**

Radius of outer circle (r) = 19 m

Circumference of outer circle = 2Ï€r = 2 x 3.14 x 19 = 119.32 m

Now radius of inner circle (r') = 19 - 10 = 9 m

âˆ´ Circumference of inner circle = 2Ï€r' = 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? **

**Solution.**

Let wheel must be rotated n times of its circumference.

Radius of wheel = 28 cm and Total distance = 352 m = 35200 cm

âˆ´ Distance covered by wheel = n x circumference of wheel

Thus, the wheel must rotate **200 times** to go 352 m.**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? **

**Solution.**

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

Radius of the circle (r) = 15 cm

A circumference of circular clock = 2Ï€r

= 2 x 3.14 x 15

= 94.2 cm

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

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