Std 7 Mathematics · Chapter 11

11. Circle

Step-by-step solutions to Practice Sets 42 and 43: circumference, radius and diameter, and arcs of a circle. Maharashtra State Board (Balbharati), Grade Seven Mathematics.

Formulas used: d = 2r, circumference c = πd = 2πr, with π = 227 (the textbook value when none is given).

Practice Set 42

1Complete the table below.

(i) r = 7 cm; d = 2 × 7 = 14 cm; c = 2 × 227 × 7 = 44 cm
(ii) d = 28 cm; r = 28 ÷ 2 = 14 cm; c = 227 × 28 = 88 cm
(iii) 616 = 227 × d ∴ d = 616 × 722 = 196 cm; r = 98 cm
(iv) 72.6 = 227 × d ∴ d = 72.6 × 722 = 23.1 cm; r = 11.55 cm

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

2If the circumference of a circle is 176 cm, find its radius.

c = 2πr
176 = 2 × 227 × r
∴ r = 176 × 744 = 28

The radius is 28 cm.

3The 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?

Circumference = 2πr = 2 × 227 × 56 = 352 m
Wire for 4 rounds = 4 × 352 = 1408 m
Cost = 1408 × 40 = 56320 rupees

The fencing will cost ₹ 56,320.

4The 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?

Circumference of wheel = πd = 227 × 1.4 = 4.4 m
Distance = 1.1 km = 1100 m (units must be the same)
Number of rotations = distancecircumference = 11004.4 = 1100044 = 250

The wheel completes 250 rotations.

Practice Set 43

1Choose 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°

Corresponding arcs together make the complete circle (360°).
m(arc AYB) = 360° − 120° = 240°

Answer: (iii) 240°

2Some arcs are shown in the circle with centre O. Write the names of the minor arcs, major arcs and semicircular arcs from among them.

QR is a diameter. The shaded arc is the minor arc QXP cut off by chord QP.

Points in order around the circle: Q, X, P, R, Y. Chord QR passes through the centre O, so it is a diameter.

Minor arcsarc QXP, arc PR

Major arcsarc QYP (also written arc QRP), arc PQR (also written arc PXR)

Semicircular arcsarc QPR (also written arc QXR), arc QYR

Each minor arc and the major arc with the same end points are corresponding arcs: arc QXP with arc QYP, and arc PR with arc PQR. The diameter QR divides the circle into the two semicircular arcs.

3In a circle with centre O, the measure of a minor arc is 110°. What is the measure of the major arc PYQ?

Measure of major arc = 360° − measure of corresponding minor arc
m(arc PYQ) = 360° − 110° = 250°

The major arc PYQ measures 250°.

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