Question

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 $c{m}^2$ $\left(Use\sqrt{3}.1.7\right)$

Answer 1

Area of one design $=$ Area of the sector $OAPB-$ Area of $△AOB$

$\frac{\theta }{360}\times \pi r^2-\frac{1}{2}{r}^2\sin \theta$

$=\frac{60}{360}\times \frac{22}{7}\times 28\times 28-\frac{1}{2}\times 28\times 28\times \sin {60}^o$

$=\frac{1}{6}\times \frac{22}{7}\times 28\times 28-\frac{1}{2}\times 28\times 28\times \frac{\sqrt{3}}{2}$

$=28\times 28(\frac{11}{21}-\frac{1.7}{4})=28\times 28\times \frac{8.3}{84}=77.47c{m}^2$

$\therefore$ Area of $6$ such designs $=77.47\times 6=464.8c{m}^2$

Hence, cost of making such designs $=464.8\times 0.35=Rs.162.69$