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As seen in the diagram below, a circular table cover includes six equal designs. Find the cost of producing the designs at a rate of ₹0.35 per $cm 2$ if the radius of the cover is 28 cm. (Use $3 = 1.7$

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₹162.66

₹168.66

₹172.66

₹178.66

answer is A.

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Detailed Solution

Given that a circular table cover includes six equal designs.
A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the design at the rate of

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the design at the rate of

Radius of the table cloth (r) = 28 cm
Total number of sectors formed due to the design = 6
Angle of one sector(

θ

)

A n g l e = 360 ° 6 A n g l e = 60 °

Area of design = Area of the sector – Area of triangle
Area of sector,

A = θ 360 ° × π r 2

Where,

θ

= angle of sector and r = radius of circle

⇒ A 1 = 60 ° 360 ° × 227 × 282

⇒ A 1 = 10348802520

⇒ A 1 = 410.66 c m 2

This is an equilateral triangle as both the sides are equal and the angle between them is

60 °

.
Area of equilateral triangle

= 34 (s i d e) 2

Substitute the value of a = OA = 28 cm in above equation,

⇒ A 2 = 34 × 282

⇒ A 2 = 1.7 4 × 784

⇒ A 2 = 1332.8 4

⇒ A 2 = 333.2 c m 2

Now,

A = A 1 − A 2

⇒ A = 410.66 − 333.2

⇒ A = 77.46 c m 2

Total area of design =

6 ×

Area of design of one sector (A)

⇒ A = 6 × 77.46

⇒ A = 464.76 c m 2

The cost of producing the designs at a rate of ₹0.35 per

cm 2

Cost of design making = Total area of design

× 0.35

Therefore, the cost of making the designs at the rate of ₹ 0.35 per

c m 2

is ₹162.66.
Therefore the answer is option (1).

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