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. (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 × πr2
(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 cm2
Area of sector OAPB = 60°/360° × πr2
= 1/6 × 22/7 × 28 × 28
= (11 × 4 × 28)/3
= 1232/3 cm2
Area of segment APB = Area of sector OAPB - Area of ΔAOB
= (1232/3 - 333.2) cm2
Area of the designs = 6 × Area of segment
= 6 × (1232/3 - 333.2) cm2
= 2464 - 1999.2 cm2
= 464.8 cm2
Cost of making 1 cm2 of designs = ₹ 0.35
∴ Cost of making 464.8 cm2 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 cm2 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 cm2 is ₹ 162.68.
☛ Related Questions:
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- 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)