Matilda is planning a walk around the perimeter of Wedge Part, which is shaped like a circular wedge, as shown below. The walk around the part is 2.1 miles, and the park has an area of 0.25 square miles. If the wedge is less than 90 degrees, what is the value of the radius, r?
pic of "wedge"
It's "as though i were British." Haven't you people heard of the subjunctive tense?
Easy stuff. Your unknowns are x (fraction of a circle) and r (the radius).
Distance around park is 2r + 2*pi*r*x
Leave it to you to express the area in terms of x and r. Two equations in two unknowns. Eliminate one of the variables and solve.
I got roughly 0.685 miles for r.
Because I have nothing better to do:
A = pi*r^2*(theta/360) = 0.25 mi^2
P = 2r+2*pi*r*(theta/360) = 2.1 mi
2 equations, 2 unknowns.
(theta/360) = 0.25/(pi*r^2)
sub into P and solve for r
2r+(2pi*r)*.25/(pi*r^2) =2.1
Might have made some mistakes in there but that\'s the general idea
Oh, would that I were.
Rene the Cart wrote:
It's "as though i were British." Haven't you people heard of the subjunctive tense?
I don't think the situation is possible. Agreeing with the equations presented in the posts above, I solved for the radius and got .47 or .15 (I'm doing this without a calculator, so there will be some rounding error). The smaller radius causes theta to be about 1400 degrees, and the larger radius causes theta to be about 140 degrees, neither of which meets the original requirement that the angle be acute.
It's obvious from the drawing that the arc and the wedge don't share the same origin, which is why the extra little side had to be added to the bottom side to intersect with the arc. Without knowing the length of this third side, this is unsolvable.
Rene the Cart wrote:
It's "as though i were British." Haven't you people heard of the subjunctive tense?
Look, we be Americans dammit. Take you're fancy grammar somewhere else.
I used a calculator and got r=.365 -> theta=215°, or r=.685 -> theta=61°
Ho Hum has your answer. Math teacher needs a new occupation.
