Question

Find the volume of the solid generated by revolving the circle x+ y = a'about X- axis.​

Answer 1

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Answer 2

Answer:

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Step-by-step explanation:

x^2+y^2 = 25 is the equation of the circle with centre (0,0) and radius 5 units.

To find the points of intersection of the line x+y=5 and the circle substitute y = 5-x in the equation of the circle.

=> x^2 + (5-x)^2 = 25

=> x^2 + 25 + x^2 - 10x = 25

=> 2x^2 -10x = 0 => 2x(x-5)=0

=> x=0 , x=5

When x= 0, y=5 and when x=5, y=0

So the points of intersection are (0,5) and (5,0).

So the required volume is

π.integ.(0 to 5){ y1^2 dx - y2^2 }dx where y1 is to be taken from the equation of the circle and Y2 is to be taken from the equation of the st.line.

So the required volume

= π integ (0 to 5){(25-x^2) - (5-x)^2} dx

= π(0 to 5){25x - (x^3)/3 + (5-x)^3 / 3}

=π{(125 - 125/3 +0) - (0 - 0 + 125/3)}

=π(125 - 125/3 - 125/3)

= 125π/3 cu.units.