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

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 cm²
= 3.14 × 16 cm²
= 50.24 cm².
Radius of inner circle (r) = 3 cm
∴ Area of the inner circle = πr²
= 3.14 × (3)² cm²
= 28.26 cm²
∴ Area of the remaining sheet = Area of the outer circle – Area of the inner circle
= 50.24 cm² – 28.26 cm²
= 21.98 cm².

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/m² (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 cm² = 36 cm²
Area of the circle cut out from the sheet = (3.14 × 2 × 2) cm² = 12.56 cm²
Area of the sheet left over = (36 – 12.56) cm² = 23.44 cm²

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 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)
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 = πr²
= 3.14(12)² m²
= 452.16 m² (> 314 m²)
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].