Finding volume of solidSuppose that a solid is formed in such a way that each cross section perpendicular to the x-axis, for 0 ≤ x ≤ 1, is a disk, a diameter of which goes from the x-axis out to the curve y = x .Find the volume of the solid.For this I use the disk formula. So π ∫ 0 1 ( x ) 2 d x . .When I do this, I get π 5 . The answer is π 8 . What am I doing wrong?

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Finding volume of solidSuppose that a solid is formed in such a way that each cross section perpendicular to the x-axis, for   0  ≤  x  ≤  1, is a disk, a diameter of which goes from the x-axis out to the curve   y  =      x  .Find the volume of the solid.For this I use the disk formula. So   π            ∫      0      1        (          x              )      2            d    x    .  .When I do this, I get             π      5      . The answer is             π      8      . What am I doing wrong?

Klecanlh · Accepted Answer

Explanation:You are told that the cross-sections perpendicular to the x-axis are disks where the diameter is from   y  =      x   to   y  =  0.- The diameter of this disk is       x  - The radius of this disk is       x        /    2- The cross-sectional area is   π  (      x        /    2      )    2  -   V  =  ∫  &quot;Cross-sectional Area&quot;       d   &quot;axis perp to cross section&quot;  V  =  π      ∫    0    1              (                                    x                    2                    )        2      d  x  =  π      ∫    0    1              x      4          d  x  =                  π                                    x            2                    8                    |        0    1    =            π      8

Dymnembalmese2n · Accepted Answer

Step 1You&#039;re doing two things wrong.One, it is explicitly saying that the diameter of each shell is       x  , so the radius would be       x        /    2Step 2Next, you&#039;re integrating wrong. The integral you have (  π      ∫    0    1    (      x        )    2      d  x) should give   π      /    2 which, multiplied by the new       1    4   from above, gives the correct answer.

Suppose that a solid is formed in such a way that each cross section perpendicular to the x-axis, for 0 leq x leq 1

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