Asolid lies between planes perpendicular to the x-axis at x=0 and x=8. the cross-sections perpendicular to the axis on the interval 0

The volume of the solid is 256 cubic units.

Step-by-step explanation:

Given:

The solid lies between planes

The cross section of the solid is a square with diagonal length equal to the distance between the parabolas .

The distance between the parabolas is given as:

Now, we know that, area of a square with diagonal 'D' is given as:

Plug in . This gives,

Now, volume of the solid is equal to the product of area of cross section and length . So, we integrate it over the length from . This gives,

Therefore, the volume of the solid is 256 cubic units.