Solids of revolution and volumes (Calculus 2)

An object has a rectangular base of dimension 3" by 9", if the 3" edge is aligned on the origin, then the height is given by y = sqrt(x). See the picture. Calculate the volume of the object.

Question

Solids of revolution and volumes (Calculus 2)

An object has a rectangular base of dimension 3" by 9", if the 3" edge is aligned on the origin, then the height is given by y = sqrt(x). See the picture. Calculate the volume of the object.

anonymous · Answer

I am thinking take the Area of a rectangle 3" * 9", and then times y^2 to get volume, as V_rect = l*w*h, but unsure. I am setting up the following integral:
$$\int\limits_{0}^{3}27y^{2} dy$$

or alternately,

$$\int\limits_{0}^{9}27\sqrt{x} dx$$

Any advice?

experimentx · Answer

is it rev??

experimentx · Answer

i don't think there is rev ... according to pic. sorry i haven't read question

anonymous · Answer

Don't know about revolution. It is just in the section name. I am trying to find the volume for this one. :)

experimentx · Answer

$$ 3'' \times \int_{0}^{9''} \sqrt x dx $$

anonymous · Answer

Ok, can you explain why please? V = A*h right?

experimentx · Answer

volume = area of base(=integration) x height(=3'')

anonymous · Answer

The base is rectangle, so I guess I was thinking area of rectangle? Confused now... :(

anonymous · Answer

Thank you amistre64 and experimentX. :D

amistre64 · Answer

take this in slice of areas; each area is defined as the limit from x=0 to x=9, bounded by y=0 and y=sqrt(x); then sum this area up as you move from 0 to 3

experimentx · Answer

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