NCERT Solutions For Class 7 Maths Chapter 11 Perimeter and Area Exercise 11.3

Table of Contents

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/m². (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

= πr²

= 3.14 x (5)²

= 3.14 x 5 x 5

= 78.5 cm²

Hence, the radius and the area of the circle area 5 cm and 78.5 cm² 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 m². [Given]

∵ Area of circular garden with radius 12 cm, covered by the sprinkler = πr²

= 3.14 x (12)² [∵ r = 12 m]

= 3.14 x 12 x 12

= 3.14 x 144

= 552.16 m²

So, Area of circular garden covered by the sprinkler = 552.13 m²

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)