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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. $0.35\ per\ cm^2$.

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Given: A round table cover has six equal designs as shown in the figure. The radius of the cover is $28\ cm$. Rate of making design is Rs. $0.35\ per\ cm^2$.

To do: To find the total cost of making the design.

Solution:

$OB=OC=28\ cm$

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

$=88\times 28$

$=2464\ cm^2$
 
$\because ABCDEF$ is a regular hexagon.

$\therefore \vartriangle OBC$ is an equilateral triangle.

$area( \vartriangle OBC)=\frac{1}{2}\times sin\theta\times side\times side=\frac{1}{2}\times\frac{\sqrt{3}}{2}\times 28\times 28=339.08\ cm^2$
 
Area of $6$ triangles $=6\times 339.08=2034.48\ cm^2$
 
Area of shaded region $=$Area of circle $-$Area of $6$ sectors $=2464-2034.48=429.52\ cm^2$
 
Rate $=0.35\ cm^2$
 
$\therefore$ Total cost of making design $=0.35\times 429.52=Rs.\ 150.33$
 

Updated on: 10-Oct-2022

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