Find the volume of the solid whose base is the region in the first quadrant bounded by y=x3, y=1, and the y-axis and whose cross-sections perpendicular to the x axis are semicircles.

The volume of a solid is the amount of space in it.

The volume of the solid is:

The given parameters are:

From the question, we understand that the cross-sections are semicircles.

This means that, the diameter (d) is:

So, we have:

The volume (V) of the solid is then calculated as:

Substitute

Expand

Integrate, with respect to x

Substitute 1 and 0, for x

Take LCM

Simplify the fraction

Hence, the volume of the solid is:

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For a given in the interval [0, 1], the corresponding cross-section is a semicircle with diameter , so the area of the cross-section would be .

The volume of the solid is then

1760 kilometers

step-by-step explanation:

multiply the amount of time the plane took to travel by it's speed