The region R is bounded by the x-axis, x=2 and y=x^2. Which of these expressions represents the volume of the solid formed by revolving R about the line x=2?

Answer 1

y = x^2
x = sqrt y = y^.5

well, you did not give us the choices.
There are basically 2

stack round plates
r = (2-y^.5)
horizontal area of plate = pi r^2
= pi (2 - y^.5)^2 = pi(4 - 4 y^.5 + y)
volume = integal y = 0 to y = 4 of
pi (4 - 4 y^.5 + y) dy

or use vertical cylinders of height y and radius (2-x)
circumference = 2 pi r = 2 pi(2-x)
height = x^2
then
integral of
x^2 (2 pi) (2-x) dx from x = 0 to x = 2

Answer 2

Which expressions can be added to find the volume of the solid figure?
Select all that apply.

A solid shape is made up of 2 attached rectangular prisms. First rectangular prism has a length of 3 m, height of 1 m, and width of 4 m. Second rectangular has a length of 3 m, height of 7 m, and width of 4 m
The total length of the shape is 6 meters.

A.4×3×7 and 1×3×4
B.4×6×7 and 1×3×3
C.1×4×7 and 4×3×6
D.4×6×1 and 6×4×3
E.4×6×3 and 7×3×3
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