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Surbhi

· started a discussion

· 1 Months ago

Hi (Question: 15964.0 )

From where did this 15 come?

Question:
A regular hexagon is inscribed in a circle of radius 5 cm. If x is the area inside the circle but outside the regular hexagon, then which one of the following is correct ? 
Options:
A) 13 cm2 < x < 15 cm2
B) 15 cm2 < x < 17 cm2
C) 19 cm2 < x < 21 cm2
D) 17 cm2 < x < 19 cm2
Solution:

We are given that, a regular hexagon is inscribed in a circle of radius 5 cm.

Here,  <AOB = 360/6 = 60

and OA = OB radii of circle

therefore \(\triangle\)AOB is an equilateral triangle.

then,  AB = 5cm.

Now, Area inside the circle but outside the regular hexagon

x=Area of circle-Area of regular hexagon

\(x = \pi r^2-({3 \sqrt{3} a^2\over 2})\)

\(x = {22 \over 7}*(5)^2-{3 \sqrt{3} \over 2}*(5)^2\)

x = 78.57-64.95

x = 13.62 cm2

Hence,  13 cm2 < x < 15 cm2 is the correct option

Knowledge Expert

· commented

· 1 Months ago

x = 13.62 cm2

Hence, 13 cm2 < x < 15 cm2 is the correct option
We chose the nearest answer.
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