RS Aggarwal Solutions: Perimeter and Area (Exercise 12B)

1: Find the circumference of a circle whose radius is
(i) 28 cm  (ii) 10.5 cm  (iii) 3.5 m
Solution: 
(i) Radius of the circle (r) = 28 cm
∴ Circumference = 2πr
= 2 × 22/7 × 28 cm
= 2 × 22 × 4 cm
= 176 cm

(ii) Radius of the circle (r) = 10.5 cm
∴ Circumference = 2πr
= 2 × 22/7 × 10.5 cm
= 2 × 22/7 × 105/10 cm
= 22 × 15 / 5 cm
= 22 × 3 cm
= 66 cm

(iii) Radius of the circle (r) = 3.5 m
∴ Circumference = 2πr
= 2 × 22/7 × 3.5 m
= 2 × 22/7 × 35/10 m
= 22 m

2: Find the circumference of a circle whose diameter is
(i) 14 cm  (ii) 35 cm  (iii) 10.5 m
Solution:
(i) Diameter of the circle (d) = 14 cm
∴ Radius (r) = d/2 = 14/2 = 7 cm
So, circumference = 2πr
= 2 × 22/7 × 7
= 2 × 22
= 44 cm

(ii) Diameter of the circle (d) = 35 cm
∴ Radius (r) = d/2 = 35/2 cm
So, circumference = 2πr
= 2 × 22/7 × 35/2
= 22 × 5
= 110 cm

(iii) Diameter of the circle (d) = 10.5 m
∴ Radius (r) = d/2 = 10.5/2 m
So, circumference = 2πr
= 2 × 22/7 × 10.5/2
= 22/7 × 105/10
= 22 × 15/10
= 330/10
= 33 m

3: Find the radius of a circle whose circumference is 176 cm.
Solution: 
Circumference of the circle = 176 cm
Let r be the radius, then
Circumference = 2πr
⇒ 176 = 2 × 22/7 × r
⇒ 2 × 22/7 × r = 176
⇒ r = 176 × 7 / 2 × 22
⇒ r = 88 × 7 / 22
⇒ r = 4 × 7
⇒ r = 28
Hence, radius of the circle is 28 cm

4: Find the diameter of a wheel whose circumference is 264 cm.
Solution: Circumference of a wheel = 264 cm
We know the diameter (d) = 2 × radius
So, let the radius = r cm
Now, circumference = 264
⇒ 2πr = 264
⇒ 2 × 22/7 × r = 264
⇒ r = 264 × 7 / 2 × 22
⇒ r = 132 × 7 / 22
⇒ r = 6 × 7
⇒ r = 42 cm
∴ The diameter (d) = 2r
= 2 × 42 cm
= 84 cm

5: Find the distance covered by the wheel of a car in 500 revolutions if the diameter of the wheel is 77 cm.
Solution: Diameter of the wheel (d) = 77 cm
∴ Radius (r) = 77/2 cm
And Circumference = 2πr
= 2 × 22/7 × 77/2 cm
= 22 × 11 cm
= 242 cm
∴ Distance cover in one revolution = 242 cm
So, distance cover in 500 revolution = 242 × 500 cm
= 121000 cm
= 1210 m