Maths-
General
Easy

Question

What is the radius of a cylinder that has a height of 3 in. and a volume of pi open parentheses 27 x squared plus 18 x plus 3 close parentheses i ?

The correct answer is: 3x + 1 is the radius of the cylinder


    using the radius and height of the cylinder .Substitute them in the formula for finding the volume and equate it with the given volume to find the value of radius of cylinder.
    ANS :-  3x+1 is the radius of the cylinder .
    Let r be the radius of the cylinder.
    Given, height is 3 in. and volume of cylinder is pi open parentheses 27 x squared plus 18 x plus 3 close parentheses i n cubed
    We know volume of cylinder = pi r squared cross times h

     pi open parentheses 27 x squared plus 18 x plus 3 close parentheses i n cubed equals pi r squared cross times 3 i n

     not stretchy rightwards double arrow 3 pi open parentheses 9 x squared plus 6 x plus 1 close parentheses equals 3 pi r squared not stretchy rightwards double arrow left parenthesis 3 x right parenthesis squared plus 2 left parenthesis 3 x right parenthesis plus left parenthesis 1 right parenthesis squared equals r squared
    As we know  here a squared plus 2 a b plus b squared equals left parenthesis a plus b right parenthesis squared text  here  end text a equals 3 x text  and  end text b equals 1 ,
    Then we getr squared equals left parenthesis 3 x plus 1 right parenthesis squared not stretchy rightwards double arrow r equals 3 x plus 1

     ∴  3x+1 is the radius of the cylinder .

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