Integration Problem (1 Viewer)

[sincred91]

Integration Problem- Need to find the volume of a frustum, with circular top and bottom B1 and B2, where h is height.

I need to derive this as the formula

h/3 (B1+B2+ sq rt (B1*B2))

i found the eqn for the line and used the formula pi (y^2) dx to find the area, but i get stuck.
Help please.

 

[Drongoski]

Integration Problem- Need to find the volume of a frustum, with circular top and bottom B1 and B2, where h is height.

I need to derive this as the formula

h/3 (B1+B2+ sq rt (B1*B2))

i found the eqn for the line and used the formula pi (y^2) dx to find the area, but i get stuck.
Help please.

Are B1 & B2 just the names of the top & bottom or are these their areas ??

 

[lolokay]

um just use a rotation of a line, eg. y = kx, between values a and b
find the expression for this volume, and the expressions for B1 and B2 in terms of the other variables, sub in. provide your working so far if you are still stuck

 

[sincred91]

well i integrate the function (2b-a/h)^2 x^2 + (2b-a/h)2ax + a2
And then i arrive at an equation whihc looks like this when i sub in B1 and B2 as functions of a^2. ie a^2=B1/pi therefore a=sq rt B1/pi
......
my answer is wrong where its
h/3 (4B2-1B1-4sqrtB1B2 h + 6 sqrt B2B1)

 

[lolokay]

i can't quite follow your working, so i'll just provide a solution