the point of this question is to make sure you fully understand the lo
The point of this question is to make sure you fully understand
the logic behind volumes by slicing (and aren't just plugging it
into a formula that doesn't really make any sense to you.)
The way to fully understand them is to understand the picture
of a slice.
The base of a solid is the region in the xy-plane between the
the lines y = 0, y = √√x, x= 1 and 2 = 3125.
Cross-sections of the solid perpendicular to the x-axis (and to
the xy-plane) are semicircles whose diameter is on the base.
(So be careful with the radius of your slices.)
To get full credit for this question, please do the following:
1. Draw a picture of the full base, labeling all relevant points.
(This might include needing to do some algebra to determine
those relevant points. Please NEATLY show that algebra work.)
2. In that base that you drew in part 1, draw a rectangle that
would represent the base of one general slice and label its
width and length with appropriate variable(s).
3. Draw the picture of the slice determined by that rectangle
you drew in part 2. Then indicate clearly what the volume of
that slice would be (In other words, what would AV be for
that slice?) Note: this volume would include variable(s).
4. Lastly, write down the integral that represents the volume
of the full solid and evaluate it with technology.
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