Finding volume of solid
Suppose that a solid is formed in such a way that each cross section perpendicular to the x-axis, for , is a disk, a diameter of which goes from the x-axis out to the curve .
Find the volume of the solid.
For this I use the disk formula. So .
When I do this, I get . The answer is . What am I doing wrong?
Answer & Explanation
You are told that the cross-sections perpendicular to the x-axis are disks where the diameter is from to .
- The diameter of this disk is
- The radius of this disk is
- The cross-sectional area is
You're doing two things wrong.
One, it is explicitly saying that the diameter of each shell is , so the radius would be
Next, you're integrating wrong. The integral you have () should give which, multiplied by the new from above, gives the correct answer.
Most Popular Questions