13. If the difference between the area of a regular hexagonal plot and the area of a circular swimming tank circumscribed in it is 26.705 m2. Find the radius of the circular swimming tank.
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the radius of the circular swimming tank = 7 m if Difference between the area of a regular hexagonal plot and the area of a circular swimming tank circumscribed in it is 26.705 m²
Step-by-step explanation:
Let say Side of hexagonal = a
and O is the center
the In Hexagonal Distance of vertex from center = side of Haxagon = a
Area of Hexagon = 6 * ( Area of Equilateral Triangle with side = a)
= 6 * (√3 / 4 )a²
= 3√3a²/2
Radius of circumscribed circle = a
Area of Circle = πr² = πa²
πa² - 3√3a²/2 = 26.705
=> a²(π - 3√3/2) = 26.705
=> a² = 49
=> a = 7
the radius of the circular swimming tank. = 7 m
A regular hexagon is inscribed in a circle. If the area of the hexagon is 24root3 cm2 find the area of the circle
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