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dmc79765
15.08.2020 •
Mathematics
the diagram shows a sector of a circle, center O,radius 5r the length of the arc AB 4r. find the area of the sector in terms of r , giving your answer in its simplest form
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Ответ:
the area of the sector in terms of r is![10r^2](/tpl/images/0722/7929/93ccd.png)
Given :
From the given diagram , the radius of the circle is 5r and length of arc AB is 4r
Lets find out the central angle using length of arc formula
length of arc =![\frac{central-angle}{360} \cdot 2\pi r](/tpl/images/0722/7929/f2f69.png)
r=5r and length = 4r
Now we replace this angle in area of sector formula
Area of sector =![\frac{angle}{360} \cdot \pi r^2\\](/tpl/images/0722/7929/cbd6a.png)
So, the area of the sector in terms of r is![10r^2](/tpl/images/0722/7929/93ccd.png)
Learn more : link
Ответ:
10r²
Step-by-step explanation:
The following data were obtained from the question:
Radius (r) = 5r
Length of arc (L) = 4r
Area of sector (A) =?
Next, we shall determine the angle θ sustained at the centre.
Recall:
Length of arc (L) = θ/360 × 2πr
With the above formula, we shall determine the angle θ sustained at the centre as follow:
Radius (r) = 5r
Length of arc (L) = 4r
Angle at the centre θ =?
L= θ/360 × 2πr
4r = θ/360 × 2π × 5r
4r = (θ × 10πr)/360
Cross multiply
θ × 10πr = 4r × 360
Divide both side by 10πr
θ = (4r × 360) /10πr
θ = 144/π
Finally, we shall determine the area of the sector as follow:
Angle at the centre θ = 144/π
Radius (r) = 5r
Area of sector (A) =?
Area of sector (A) = θ/360 × πr²
A = (144/π)/360 × π(5r)²
A = 144/360π × π × 25r²
A = 144/360 × 25r²
A = 0.4 × 25r²
A = 10r²
Therefore, the area of the sector is 10r².
Ответ:
the answer is 180
Step-by-step explanation: