Perimeter and Area - Solutions 3
CBSE Class –VII Mathematics
NCERT Solutions
Chapter 11 Perimeter and Area (Ex. 11.3)
NCERT Solutions
Chapter 11 Perimeter and Area (Ex. 11.3)
Question 1. Find the circumference of the circles with the following radius:
(a) 14 cm
(b) 28 mm
(c) 21 cm
Answer: (a) Circumference of the circle = = = 88 cm
(b) Circumference of the circle = = = 176 mm
(c) Circumference of the circle = = = 132 cm
Question 2. Find the area of the following circles, given that:
(a) radius = 14 mm
(b) diameter = 49 m
(c) radius 5 cm
Answer: (a) Area of circle = = = 22 x 2 x 14 = 616 mm2
(b) Diameter = 49 m
radius = = 24.5 m
Area of circle = = = 22 x 3.5 x 24.5 = 1886.5 m2
(c) Area of circle = = = cm2
Question 3. If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet.
Answer: Circumference of the circular sheet = 154 m
= 154 m
= 24.5 m
Now, Area of circular sheet = = = 22 x 3.5 x 24.5 = 1886.5 m2
Thus, the radius and area of circular sheet are 24.5 m and 1886.5 m2 respectively.
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 costs of the rope, if it cost Rs. 4 per meter.
Answer: Diameter of the circular garden = 21 m
Radius of the circular garden = m
Now, Circumference of circular garden = = = 2 x 11 x 3 = 22 x 3 = 66 m
The gardener makes 2 rounds of fence so the total length of the rope of fencing
= 2 x = 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
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.
Answer: Radius of circular sheet (R) = 4 cm and radius of removed circle (r) = 3 cm
Area of remaining sheet = Area of circular sheet – Area of removed circle
= =
= =
= 3.14 x 7 = 21.98 cm2
Thus, the area of 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 Rs. 15.
Answer: Diameter of the circular table cover = 1.5 m
Radius of the circular table cover = m
Circumference of circular table cover = = = 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.
Question 7. Find the perimeter of the adjoining figure, which is a semicircle including its diameter.

Answer: Diameter = 10 cm
Radius = = 5 cm
According to question,
Perimeter of figure = Circumference of semi-circle + diameter
= + D = =
= = 25.71 cm
Thus, the perimeter of the given figure is 25.71 cm.
Question 8. Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is Rs. 15/m2.
Answer: Diameter of the circular table top = 1.6 m
Radius of the circular table top = 0.8 m
Area of circular table top = = 3.14 x 0.8 x 0.8 = 2.0096 m2
Now cost of 1 m2 polishing = Rs. 15
Then cost of 2.0096 m2 polishing = 15 x 2.0096 = Rs. 30.14 (approx.)
Thus, the cost of polishing a circular table top is Rs. 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?
Answer: Total length of the wire = 44 cm
the circumference of the circle = = 44 cm
= 7 cm
Now Area of the circle = = = 154 cm2
Now the wire is converted into square.
Then perimeter of square = 44 cm
4 x side = 44 side = = 11 cm
Now area of square = side x side = 11 x 11 = 121 cm2
Therefore, on comparing the area of circle is greater than that of square, so the circle enclosed more area.
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.

Answer: Radius of circular sheet (R) = 14 cm and Radius of smaller circle = 3.5 cm
Length of rectangle = 3 cm and breadth of rectangle = 1 cm
According to question,
Area of remaining sheet = Area of circular sheet – (Area of two smaller circles + Area of rectangle)
=
=
= 22 x 14 x 2 – [44 x 0.5 x 3.5 + 3]
= 616 – 80
= 536 cm2