Asked by Jonel
Part of the stage decoration is a "fan" shape and is to be covered with a white cloth. If the radius of the fan is x+3 and its area is 198 meter squared, what is the dimension of the fan?
Answers
Answered by
Steve
The fan is a sector of a circle. That means that
198 = 1/2 (x+3)^2 θ
Unless you know how much of a circle the fan occupies (that is, what is θ, compared to 2π), there's no way to solve for x.
If the fan is a half-circle, θ=π, so
198 = 1/2 (x+3)^2 (π/2)
(x+3)^2 = 198*4/π = 252.10
x+3 = 15.88
x = 12.88
Now use that to decide what the "dimension" is.
198 = 1/2 (x+3)^2 θ
Unless you know how much of a circle the fan occupies (that is, what is θ, compared to 2π), there's no way to solve for x.
If the fan is a half-circle, θ=π, so
198 = 1/2 (x+3)^2 (π/2)
(x+3)^2 = 198*4/π = 252.10
x+3 = 15.88
x = 12.88
Now use that to decide what the "dimension" is.
Answered by
Steve
oops - I plugged in π/2 instead of π.
The solution above is correct if the fan is 1/4 of a circle.
The solution above is correct if the fan is 1/4 of a circle.
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