Question

Question 1 Let R be the region enclosed by the positive x-axis, the positive y-axis, and the curve y = (9- x2,1/2. A solid is generated by rotating about x-axis. What is the volume of the solid? give exact answer in term of Pi.(example:a pi) Y Y = 19 22 R 0 3

Answer 1

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Answer 2

SOLUTON :

Region R bounded by x-axis, y-axis and y = sqrt(9 - x^2) .

It is rotated about x-axis. To find volume of the solid generated.

Let us take a strip of height y , width dx . If it is rotated about x-axis,

volume generated = dV = π y^2 dx 

x varies from 0 to 3 .

So, 

Volume of solid generated, V  

   3                        3

= ∫ π (y^2) dx = π  ∫ (9 - x^2) dx  

   0                        0

                            3

= π [ 9x - x^3 / 3 ]

                           0

= π [ (9*3 - 3^3 / 3) - 0 ]\

= π [ 27 - 9 ]

= 18 π. (ANSWER)