# 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...

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)`

`rArr 100=10pir+pir^2`

`rArrpir^2+10pir-100 = 0`

`r= (-10pi+-sqrt((10pi)^2-4*pi*(-100)))/(2*pi)`

`=(-10pi+-sqrt(100pi^2+400pi))/(2pi)`

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`

`=2.538633`

=2.54 inches (approximation upto two decimal places).

**Therefore, the radius of the base of the cylinder is 2.54 inches.**