Acircular tablecloth of radius 30cm is to made .There should be two circular designed strips of width 5 cm each and width in between these strips is to be 5cm.. The radius of the inner circular plane portions is 10 cm. Find the total cost of making the two designed strips at the rate of Rs 0.75 per cm2.
Here OA = 10 cm, OB = 10 cm + 5 cm = 15 cm, OC = 10 cm + 5 cm + 5 cm = 20 cm and OD = 10 cm + 5 cm + 5 cm + 5 cm = 25 cm
Area of the inner strip
= π (OB2 – OA2)
= π [(15 cm)2 – (10 cm)2]
= π (225 – 100) cm2
= 125 π cm2
Area of the outer strip
= π (OD2 – OC2)
= π [(25 cm)2 – (20 cm)2]
= π ( 625 cm2 – 400 cm2)
= 225 π cm2
Total area of the two strips = 125 π cm2 + 225 π cm2 = 350 π cm2
Cost of making 1 cm2 strip = 0.75
∴ Cost of making 350 π cm2 strip
= Rs 0.75 × 350 π
Thus, the total cost of making two designed strips is Rs 825.