Total number of equal designs = 6

AOB= \( \dfrac{360°}{6} \) = 60°

Radius of the cover = 28 cm

Cost of making design = ₹ 0.35 per cm^{2}

Since the two arms of the triangle are the radii of the circle and thus are equal,

and one angle is 60°, ΔAOB is an equilateral triangle.

So, its area will be (\( \dfrac{\sqrt{3}}{4}\))×a^{2} sq. units

Here, a = OA

Area of equilateral ΔAOB = (\( \dfrac{\sqrt{3}}{4}\))×28^{2 }= 333.2 cm^{2}

Area of sector ACB = (\(\dfrac{ 60°}{360°}
\))×πr^{2 }cm^{2}

= 410.66 cm^{2}

So, area of a single design = area of sector ACB – area of ΔAOB

= 410.66 cm^{2} – 333.2 cm^{2 }= 77.46 cm^{2}

Area of 6 designs = 6×77.46 cm^{2 }= 464.76 cm^{2}

So, total cost of making design = 464.76 cm^{2 }×Rs.0.35 per cm^{2}

= Rs. 162.66

Answered by Abhisek | 1 year agoProve that the area of a circular path of uniform width hsurrounding a circular region of radius r is πh(2r + h).

A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.

The outer circumference of a circular race-track is 528 m. The track is everywhere 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre

A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of ₹25 per square metre (Use π = 3.14)

A path of width 3.5 m runs around a semicircular grassy plot whose perimeter is 72 m. Find the area of the path.