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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, find the cost of making the designs at the rate of Rs. 0.35 per $cm^2$. (Use $\sqrt3= 1.7$)"

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:

We have 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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