Question 265285
First convert 6 inches into 1/2 ft. Now all units are in feet.
let x feet be the uniform length of the concrete.
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we can find the area of the concrete as
{{{pi*(8+x)^2 - pi*8^2 = 16*pi*x + pi*x^2}}}
and then the volume os area of circle times height. So, we get
{{{(1/2)*(16*pi*x + pi*x^2) = 27}}}
multiply by 2 to get
{{{16*pi*x + pi*x^2) = 54}}}
subtract 54 to get
{{{16*pi*x + pi*x^2) - 54 = 0}}}
by quadratic, we get x as
x ~ 1.0105 feet.