Mathematics Solutions Solutions for Class 7 Maths Chapter 12 Circle are provided here with simple step-by-step explanations. These solutions for Circle are extremely popular among Class 7 students for Maths Circle Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of Class 7 Maths Chapter 12 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Solutions Solutions. All Mathematics Solutions Solutions for class Class 7 Maths are prepared by experts and are 100% accurate.

#### Question 1:

Complete the table below

 Sr. No. Radius (r) Diameter (d) Circumference (c) (i) 7 cm .................... ................. (ii) ............ 28 cm .............. (iii) .............. ............... 616 cm (iv) ........... ............. 72.6 cm

(i) Radius, r = 7 cm
Diameter, d = 2r = 2 × 7 = 14 cm
∴ Circumference, c = πd
$\frac{22}{7}$ × 14
= 22 × 2
= 44 cm

(ii) Diameter, d = 28 cm
Radius, r$\frac{d}{2}$ = $\frac{28}{2}$ = 14 cm
∴ Circumference, c = 2πr
= 2 × $\frac{22}{7}$ × 14
= 88 cm

(iii) Circumference, c = 616 cm
Now, c = 2πr     (where 'r' is the radius)
⇒616 = 2 × $\frac{22}{7}$ × r
r = 616 × $\frac{1}{2}$ × $\frac{7}{22}$
r = 98
Diameter, d = 2r = 2 × 98 = 196 cm

(iv) Circumference, c = 72.6 cm
Now, c = 2πr     (where 'r' is the radius)
⇒72.6 = 2 × $\frac{22}{7}$ × r
r = 72.6 × $\frac{1}{2}$ × $\frac{7}{22}$
r = 11.55
Diameter, d = 2r = 2 × 11.55 = 23.1 cm

The complete table is shown below.

 Sr. No. Radius (r) Diameter (d) Circumference (c) (i) 7 cm 14 cm 44 cm (ii) 14 cm 28 cm 88 cm (iii) 98 cm 196 cm 616 cm (iv) 11.55 cm 23.1 cm 72.6 cm

#### Question 2:

If the circumference of a circle is 176 cm, find its radius.

Circumference, c = 176 cm
Now, c = 2πr    (where 'r' is the radius of circle)
⇒176 = 2 × $\frac{22}{7}$ × r
r = 176 × $\frac{1}{2}$ × $\frac{7}{22}$
r = 28
∴ Radius of the circle = 28 cm

#### Question 3:

The radius of a circular garden is 56 m. What would it cost to put a 4-round fence around this garden at a rate of 40 rupees per metre ?

Radius of the circular garden, r = 56 m
Circumference of the circular garden, c = 2πr
= 2 × $\frac{22}{7}$ × 56
= 352 m
∴ Length of the wire needed for one round of fencing = c = 352 m
Cost of one round of fencing = length of wire × cost per metre
= 352 × 40
= 14080 rupees
Cost of four round of fencing = 4 × 14080 = 56320 rupees

#### Question 4:

The wheel of a bullock cart has a diameter of 1.4 m. How many rotations will the wheel complete as the cart travels 1.1 km ?

Diameter of the wheel, d = 1.4 m
Circumference, c = πd
$\frac{22}{7}$ × 1.4
= 4.4 m
When the wheel completes 1 rotation, it covers a distance that is equal to its circumference.
So, number of rotations taken by the wheel to cover 4.4 m = 1
Now, the wheel covered a total distance of 1.1 km.
We know that, 1 km = 1000 m
∴ 1.1 km = 1.1 × 1000 m = 1100 m
∴ Total number of rotations taken by wheel =
$\frac{1100}{4.4}$
$\frac{11000}{44}$
= 250
Hence, the wheel completes 250 rotations to cover a distance of 1.1 km.

#### Question 1:

Choose the correct option.
If arc AXB and arc AYB are corresponding arcs and m(arc AXB) = 120° then m(arc AYB) =

(i) 140°   (ii) 60°   (iii) 240°  (iv) 160°

Consider that arc AXB is the minor arc and arc AYB is the corresponding major arc.
It is known that, measure of major arc = 360 − measure of the corresponding minor arc.
We have, m(arc AXB) = 120°.
So, m(arc AYB) = 360 − m(arc AXB) = 360 − 120 = 240
Hence, the correct answer is option (iii).

#### Question 2:

Some arcs are shown in the circle with centre ‘O’. Write the names of the minor arcs, major arcs and semicircular arcs from among them.

Minor arc : An arc of a circle having measure less than 180.
Major arc : An arc of a circle having measure greater than 180.
Semicircular arc : An arc of a circle having measure equal to 180.

Names of minor arcs :
(i) arc PXQ
(ii) arc PR
(iii) arc RY
(iv) arc XP
(v) arc XQ
(vi) arc QY

Names of major arcs :
(i) arc PYQ
(ii) arc PQR
(iii) arc RQY
(iv) arc XQP
(v) arc QRX

Names of semicircular arcs :
(i) arc QPR
(ii) arc QYR

#### Question 3:

In a circle with centre O, the measure of a minor arc is 110°. What is the measure of the major arc PYQ?

Suppose PQ is the minor arc and then m(arc PQ) = 110.
We know that, measure of major arc = 360 − measure of corresponding minor arc.
∴ m(arc PYQ) = 360 − m(arc PQ)
=  360 − 110
= 250
Hence, the measure of major arc PYQ is 250.

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