# 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 designs at the rate of Rs. 0.35 per $$cm^2$$ . (Use $$\sqrt{3} \ = \ 1.7$$)

Clearly from the figure,

Area of one design

= Area of the sector AOB - Area ( $$∆ \ AOB$$ )

$$= \ \frac{ \theta }{360} \ × \ \pi r^2 \ - \frac{1}{2} \ × \ (r)^2 \ × \ sin60°$$, where $$r \ = \ 28$$ cm

$$= \ \frac{60}{360} \ ×$$ $$\frac{22}{7} \ × \ (28)^2$$ $$- \ \frac{1}{2} \ × \ (28)^2 \ × \ \frac{ \sqrt{3}}{2}$$

$$= \ \frac{1232}{3} \ - \ 333.2$$

$$= \ \frac{1232 \ - \ 999.6}{3}$$

$$= \ \frac{232.4}{3}$$cm2

Area of 6 such design $$= \ 6 \ × \ \frac{232.4}{3} \ = \ 464.8$$cm2

Cost of making such designs @ Rs. 0.35 per cm2

= Rs $$0.35 \ × \ 464.8$$

= Rs 162.68