MHB Finding the outer diameter of an annulus

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To find the outer diameter of a pipe with an inner diameter of 28 mm and a wall cross-section area of 4.5 cm², first convert the inner diameter to centimeters, resulting in 2.8 cm. The area of the annulus is calculated by subtracting the area of the inner circle from the area of the outer circle, leading to the equation 4.5 = πr² - π(1.4)². Solving this equation for the outer radius r will yield the necessary dimensions. The final step involves doubling the outer radius to determine the outer diameter.
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A pipe with a circular cross-section area has the inner diameter of 28 mm. How big should the pipe's outer diameter be, if the cross section area of the pipe's wall is 4.5 cm2?

I have been trying to solve this for ages, but failed so far... Can someone help?
 
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Re: Help with geometry question needed

linapril said:
A pipe with a circular cross-section area has the inner diameter of 28 mm. How big should the pipe's outer diameter be, if the cross section area of the pipe's wall is 4.5 cm2?

I have been trying to solve this for ages, but failed so far... Can someone help?

Let's first make sure that the units are consistent. $28\text{ mm} = 2.8\text{ cm}.$

Suppose the outer radius is $r.$ The area of a cross section will be the area of the outer circle minus the area of the inner circle. So we have
\[4.5 = \pi r^2 - \pi(1.4)^2.\]
Solve for $r.$
 
Re: Help with geometry question needed

Thank you!
 
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