help with super easy integration questions! (1 Viewer)

[talisman]

Q1: A hemispherical bowl of radius a units is filled with water to a depth of a/2 units Find, by integration, the volume of the water.

I keep getting the answer 7a^3pi/24

The answer is 5a^3pi/24

I must be struck by an indefinable stroke of dumbness of (hopefully) the answer might be wrong.

I would use the LaTex equation editor thing, but I don't really know how to post it on BOS. I tried quotation marks, but that doesn't work!

 

[RealiseNothing]

Q1: A hemispherical bowl of radius a units is filled with water to a depth of a/2 units Find, by integration, the volume of the water.

I keep getting the answer 7a^3pi/24

The answer is 5a^3pi/24

I must be struck by an indefinable stroke of dumbness of (hopefully) the answer might be wrong.

I would use the LaTex equation editor thing, but I don't really know how to post it on BOS. I tried quotation marks, but that doesn't work!

Put

 

[darkphoenix]

make the volume spin at y axis
x^2=a^2 - y^2
where limits are y= a and y= a/2

integrate that: a^2y- y^3/3
then substitute a and a/2
subtract them and you get 5a^3pi/24

 

[talisman]

i see my problem in my working now. thanks guys!