Question

question about volume!!

Answer 1

@DanJS last question if you could help me!!!

Answer 2

is it 1024/3?

Answer 3

how is the equation of a circle x^2+y^2+16?
is it typo? it should be x^2+y^2 =16, right?

Answer 4

yeah i think it should be = also

Answer 5

if it so, the cylinder with the radius of the base = 4, and the height is 4 also, hence the volume is 16pi *4 = 201.056 , to me. :)

Answer 6

@perl do you know?!

Answer 7

yess

Answer 8

solve for x first
x = +/- sqrt( 16-y^2)

2*integral ( sqrt(16-y^2)-(-sqrt(16-y^2) ) ^2 on y=0..4

which becomes

2*integral (2*sqrt(16-y^2))^2 , y = 0..4

Answer 9

thank you for the explanation!!

Answer 10

or you can integrate from -4 to 4 directly

Answer 11

we are given x^2+y^2=16

solve for x first

x = +/- sqrt( 16-y^2)
The 'right half' semicircle is the equation
x = sqrt(16-y^2)
the 'left half' semicircle is the equation
x = -sqrt(16-y^2)

we use the form
integral A(y)dy

Here A(y) = ((sqrt(16-y^2)-(-sqrt(16-y^2)))^2
which becomes
A(y) = (sqrt(16-y^2) +sqrt(16-y^2))^2
A(y) = (2*sqrt(16-y^2))^2

So we have

integral A(y)dy on y=-4..4

integral (2*sqrt(16-y^2))^2 dy on y=-4..4

Answer 12

A(y) stands for area at y