Question 530396
A sector-shaped piece of canvas is wrapped around a frame to make a right circular cone which is being used as a tent. If the canvas has an area of 11.9 m2, and a radius of 2.33 m, determine the value of the subtended angle (θ, in radians), and the base diameter and height of the finished tent. 
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Draw a picture of the pie-shaped sector.
It is a piece of a circle with area = (pi)r^2 = pi*2.33^2 m^2
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The sector is 11.9/(pi*2.33^2) = 0.6977 the area of the circle
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Therefore the subtended angle is 0.6977*2(pi) = 4.3838 radians
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Area of the cone = (1/3)pi*r^2*h = 11.9 m^2
(1/3)pi*2.33^2*h = 11.9 m^2
height =  2.0932 meters
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diameter = ?
radius^2 = 2.33^2-2.0932^2
r = 1.0235
diameter = 2*1.0235 = 2.0469 meters
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Cheers,
Stan H.