The volume of the solid obtained by rotating the region bounded by y=x, y=lnx, x=1, and x=3 about the line y-axis can be computed using the method of cylindrical shells. Answer the following questions.

Volume of solid = 74.454pi or 233.94

Step-by-step explanation:

The detailed calculation and appropriate integration to ge the volume of the solid is as shown in the attachment.

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!

answer:   rotate 270° clockwise about (7, 1) and reflect across the line x = 7

step-by-step explanation:

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