Question

A round table cover has six equal designs as shown in the figure. If the radius of the cover is 28 cm,then find the cost of making the design at the rate of rs/. 0.35 per $c{m}^2$.

Answer 1

$OB=OC=28cm$

Area of circle $=\pi r^2=\frac{22}{7}\times 28\times 28$

$=88\times 28$

$=2464c{m}^2$

Since, ABCDEF is a regular hexagon

$\therefore \Delta OBC$ is an equilateral $\Delta$

$ar\left(\Delta OBC\right)=\frac{\sqrt{3}}{4}\times 28\times 28=339.08c{m}^2$

Area of 6 triangles $=6\times 339.08=2034.48c{m}^2$

Area of shaded region = Area of circle - Area of 6.

$=2464-2034.48=429.52c{m}^2$

Rate $=0.35c{m}^2$

$\therefore$ Rate $=0.35\times 429.52=Rs.150.33$