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# A round table cover has six equal designs as shown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs. 0.35 per cm^{2}. (Use √3 = 1.7)

**Solution:**

We know that, in a circle with radius r and the angle at the center with degree measure θ,

(i) Area of the sector = θ/360 × πr^{2}

(ii) Area of the segment = Area of the sector - Area of the corresponding triangle

Visually it is clear from the diagram that the designs are segments of the circle.

∴ Area of the design = Area of 6 segments of the circle.

Since the table cover has 6 equal design, therefore angle of each sector at the center = 360°/6 = 60°

Consider segment APB. Chord AB subtends an angle of 60° at the center.

∴ Area of segment APB = Area of sector AOPB - Area of ΔAOB

Consider ΔAOB

OB = OA (radii of the circle)

∠OAB = ∠OBA (angles opposite to equal sides in a triangle are equal)

∠AOB + ∠OAB + ∠OBA = 180° (angle sum property of a triangle)

2∠OAB = 180° - 60° (Since, ∠AOB = 60°)

∠OAB = 120°/2 = 60°

∴ ΔAOB is an equilateral triangle

Area of ΔAOB = √3/4 (side)^{2}

= √3/4 (28)^{2} (Since the side of the triangle = radii of the circle = 28 cm)

= √3 × 7 × 28

= 196√3

= 196 × 1.7

= 333.2 cm^{2}

Area of sector OAPB = 60°/360° × πr^{2}

= 1/6 × 22/7 × 28 × 28

= (11 × 4 × 28)/3

= 1232/3 cm^{2}

Area of segment APB = Area of sector OAPB - Area of ΔAOB

= (1232/3 - 333.2) cm^{2}

Area of the designs = 6 × Area of segment

= 6 × (1232/3 - 333.2) cm^{2}

= 2464 - 1999.2 cm^{2}

= 464.8 cm^{2}

Cost of making 1 cm^{2} of designs = ₹ 0.35

∴ Cost of making 464.8 cm^{2} of designs

= ₹ 0.35 × 464.8

= ₹ 162.68

**☛ Check: **Class 10 Maths NCERT Solutions Chapter 12

**Video Solution:**

## A round table cover has six equal designs as shown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs. 0.35 per cm².

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.2 Question 13

**Summary:**

The cost of making 464.8 cm^{2} area of designs of a round table cover if a round table cover has six equal designs with a radius of the cover as 28 cm at the rate of Rs. 0.35 per cm^{2} is ₹ 162.68.

**☛ Related Questions:**

- Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
- Find the area of a quadrant of a circle whose circumference is 22 cm.
- The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
- A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding : (i) minor segment (ii) major sector. (Use π = 3.14)

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