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The formula for the surface area is: A = 2(pie)(r)(h) + 2(pie)(r)^2
If the height of a cylinder is 10 inches, and the surface area is 200 sq. inches, determine the length of the radius. Round your answer to 2 places.
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Surface area of the cylinder is given by, `A = 2pirh + 2pir^2`
simplifying, `A = 2pir(h+r)`
Here, h, the height of a cylinder is 10 inches, and A, the surface area is 200 sq. inches. Let the radius of the base of the cylinder be r inches.
putting the values in the simplified equation we get,
`200 = 2pir (10+r)`
`rArrpir^2+10pir-100 = 0`
Putting the value of pi,
`r = ( -31.41593+-sqrt(986.9804+1256.637))/6.283185`
`= ( -31.41593+-sqrt(2243.598))/6.283185`
` ` `=(-31.41593+-47.36663)/6.283185`
`=(-31.41593+47.36663)/6.283185` (the other solution would yield a negative value for radius, which is impossible, hence discarded)
`rArr r = 15.9507/6.283185`
=2.54 inches (approximation upto two decimal places).
Therefore, the radius of the base of the cylinder is 2.54 inches.
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