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Reika [66]
2 years ago
12

In a​ circle, a 225 degrees sector has area 490pi in2. What is the radius of the​ circle?

Mathematics
1 answer:
Nutka1998 [239]2 years ago
7 0
We know that

area of a sector=(∅*pi/360°)*r²--------> when ∅ is in degree
r=√[360°*(area of a sector)/(∅*pi)]

area of a sector=(∅/2)*r²--------> when ∅ is in radians
r=√[2*(area of a sector)/∅]

let's calculate the radius of the two ways

1) r=√[360°*(area of a sector)/(∅*pi)]
area of a sector=490*pi in²
∅=225°
 r=√[360°*(490*pi)/(225°*pi)]-------> r=√784-----> r=28 in

2) r=√[2*(area of a sector)/∅]
area of a sector=490*pi in²
∅=225°-----> convert to radians-----> ∅=225°*pi/180-----> ∅=1.25*pi
r=√[2*(490*pi)/(1.25*pi)]----> r=√[980/1.25]---> r=√784----> r=28 in

the answer is 
the radius is 28 in
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You can make an equation with this information using a variable for the number of days and solve for that variable. Here we can use d to represent days.

Ryan can build 4 desks in a day, so you could express his production as 4d.

Larry can build 4 desks in 2 days, so you could say he makes 2 desks in 1 day, expressed as 2d.

If Larry starts work one day before Ryan, he's made an extra 2 desks. To get 32 desks, you need to add together those 2 desks Larry made, however many desks Larry can make, and however many desks Ryan can make:

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