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

December 26, 2021

These NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Ex 11.3 Questions and Answers are prepared by our highly skilled subject experts.

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

Question 1.
Find the circumference of the circles with the following radius: (Take π = 22/7)
(a) 14 cm
(b) 28 mm
(c) 21 cm
Answer:
(a) Radius of the circle (r) = 14 cm
Circumference of the circle = 2πr units
= 2 × 22/7 x 14 cm
= 2 × 22 × 2 cm
= 88 cm

(b) Radius of the circle = 28 mm.
.’. Circumference of the circle = 2πr units
= 2 × 22/7 × 28 mm
= 2 × 22 × 4 mm
= 176 mm

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

(b) Diameter of the circle = 49 m.

Question 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)
Answer:
Circumference of a circle = 154 m

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 of fence. Also, find the cost of the rope, if it cost ₹ 4 per meter. (Take π = 22/7)

Length of the rope required for one round fence = 66 m
Length of the rope required for two round fence = 66 m × 2 m = 132 m
Cost of rope per meter = ₹ 4
Total cost of the rope = ₹132 × 4 = ₹ 528

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)

Answer:
Radius of outer circle (R) = 4 cm
Radius of inner circle (r) = 3 cm
= Area of the outer circle – Area of the inner circle
Area of the remaining sheet = n (R² – r²)
= 3.14 (4² – 3²)
= 3.14 × (16-9)
= 3.14 x 7 = 21.98 cm²
So, the area of the remaining sheet is 21.98 cm².

Question 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)
Answer:

Question 7.
Find the perimeter of the given figure, which is a semicircle including its diameter.

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)
Answer:
Diameter of the table-top = 1.6 m
Radius of the table-top = 1.6/2 = 0.8m
Area of the table-top = πr² sq. m
= 3.14 × 0.8 × 0.8 m² = 2.0096 m²
Rate of Polishing = ₹ 15 per m²
Cost of polishing the table-top = ₹ 2.0096 × 15 =₹ 30.14 (approx.)

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 or the square?
(Take π = 22/7)
Answer:
Length of the wire = 44 cm
Let the radius of the circle be r.
Circumference of the circle = 44 cm

Since, the wire is rebent to form a square. Perimeter of the square = Length of the wire
4a = 44
[Perimeter of a square = 4a] 44
a = 44/6 = 11 cm 6
Side of a square =11 cm
Area of the square = side × side
= 11 × 11 cm² = 121 cm²
154 cm² > 121 cm²
Area of the circle > Area of the square
∴ The circle encloses greater area.

Question 10.
From a circular card sheet of radius 14cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed, (as shown in the given figure). Find the area of the remaining 22
sheet. (Take π = 227)

Answer:
Radius of the circular card sheet =14 cm
Area of the sheet = πr² sq m
= 22/7 × 14 × 14 cm²
= 22 × 2 × 14 cm2 = 616 cm²
Radius of a small circle = 3.5 cm
Area of 2 small circles = 2 × πr² sq m
= 2 × 22/7 × 3.5 × 3.5 cm²
= 2 × 22 × 0.5 × 3.5 cm = 77 cm²
Length of a small rectangle = 3 cm
Breadth of a small rectangle = 1 cm.
Area of small rectangle = l × b sq.m
= 3 × 1 cm² = 3 cm²
Area of the remaining sheet = Area of the circular sheet – (Area of two small circles + Area of rectangle)
= 616 cm²– (77 + 3)cm²
= 616 cm² – 80 cm² = 536 cm²
∴ Required area of the remaining sheet = 536 cm²

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 left over aluminium sheet? (Take π = 3.14)
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)
Answer:
Side of the square = 6 cm
Area of the square = side × side
= 6 cm × 6 cm = 36 cm²

Radius of the circle cut out from the sheet = 2 cm
Area of the circle = πr² sq.m
= 3.14 × 2 × 2 cm² = 12.56 cm²
Area of the remaining sheet
= 36 cm² – 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 n = 3.14)
Answer:
Let the radius of the circle be ‘r’
Circumference of a circle = 31.4 cm

Area of the circle = 2πr² sq. units = 3.14 × 5 × 5 cm² = 78.5 cm²

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)
Answer:
Diameter of the flower bed = 66 m

width of the surrounding path = 4 m
Radius of the outer circle (R)
= 33 m + 4 m
(R) = 37 m
Area of the pathway = Area of the outer circle – Area of the inner circle
= πR² – πr²
= π(R² – r²) sq. units
= 3.14 (37² – 33² ) m²
= 3.14 (37 + 33) (37 – 33) m²
= 3.14 × 70 × 4 m²
= 3.14 × 280 m²
= 879.2 m²
Thus, the area of the path = 879.2 m²

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)
Answer:
Let the radius of the garden be ‘r’
Area of the circular garden = 314 m²

Radius of the area covered by the sprinkler = 12 m
Since 12 m > 10 m
The sprinkler covers an area beyond the garden.
Yes, the entire garden is covered by the sprinkler.

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

Answer:
Radius of the outer circle (R) = 19 m.
Circumference of the outer circle
= 2πr unit
= 2 × 3.14 × 19 m
= 119.32 m
Radius of the inner circle (r)
= 19- 10 = 9m
Circumference of the inner circle
= 2π = 2 × 3.14 × 9 m = 56.52 m

Question 16.

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)
Answer:
Length of the minute hand =15 cm
radius of the circle (r) = 15 cm
(made by the tip of the minute hand)
Perimeter of the circle = 2πr units
= 2 × 3.14 × 15 cm = 94.2 cm
Distance covered by the minute hand = 94.2 cm

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

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