Question

What was the calculus formula to determine the volume of a solid? I don't mean solid of revolution. Just regular solid.

Answer 1

volumes of cross sections

Answer 2

Are you sure you aren't looking for:
\[\text{ Volume }=\int\limits_a^bA(x) dx \text{ where } A(x) \text{ is the area of the cross section } ?\]

Answer 3

yes that is it ! thank you !

Answer 4

that's also the formula used in solids formed by revolution of some curve about some axis

Answer 5

u forget to square it..i think @freckles

Answer 6

you know where we take circles as the cross section

Answer 7

no A(x) is the area
you don't want to square the area

Answer 8

o ok

Answer 9

if the cross section is a circle then A(x)=pi*r^2

Answer 10

where r is a function of x

Answer 11

though we could look at things in terms of y too
not just x

Answer 12

you know depending on what suits us better

Answer 13

but how is that the formula for solids of revolution? I mean the formula for solids of revolution is \[\int\limits_{a}^{b}(\pi*f(x)^2) dx\]

Answer 14

i think the f(x) is actually the radius

Answer 15

f(x) is the function

Answer 16

i mean the height of the funtion

Answer 17

yes which is intern the radius
so A=pi*r^2

Answer 18

and freckles just use the Area instead...i think

Answer 19

I guess i am kind of confuse lol

Answer 20

ok lets wait on till @freckles come online...

Answer 21

what's the question?

Answer 22

area of a circle is what I called A(x)

Answer 23

or the are of the cross section is A(x)

Answer 24

if the cross section is a circle then A(x) is pi*r^2
where r is the radius
f(x) is the distance from the curve to the x-axis
so f(x) is the radius if the axis of rotation is the x-axis

Answer 25

Say we want to take this curve on [a,b] and rotate it about the x-axis