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.
I've found the first part of the question - subtended angle of 4.38.
I'm not sure how to solve for the base and height. Can you please lead me in the right direction
Thanks!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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