Finding the outer diameter of an annulus

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SUMMARY

The discussion focuses on calculating the outer diameter of a pipe with an inner diameter of 28 mm and a wall cross-sectional area of 4.5 cm². The inner diameter is converted to centimeters, resulting in 2.8 cm. The formula used to find the outer radius involves subtracting the area of the inner circle from the outer circle, leading to the equation 4.5 = πr² - π(1.4)². Solving this equation provides the necessary dimensions for the pipe.

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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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