Volumes Question (2 Viewers)

[cutemouse]

Hello,

Could someone please do this for me? Thanks

A solid has a square base of side 6m. Each section of the solid at a height hm above the base is a square whose side varies as (4-h). Find the volume of the solid.

The answer is 48m³, and I don't know how to get to it. Could someone please show their working?

Thanks again!

 

[azureus88]

The volume is just a square pyramid height 4m and base 6m by 6m. Slicing the pyramid parallel to base gives square slices of side s and width dh with h being height of slice above base.

By using similar triangles,

[maths]\frac{s/2}{3}=\frac{4-h}{4}[/maths]

[maths]s=\frac{3}{2}(4-h)[/maths]

[maths]\delta V=s^2\delta h=\frac{9}{4}(4-h)^2[/maths]

[maths]V=\lim_{\delta h\rightarrow 0}\frac{9}{4}(4-h)^2[/maths]

[maths]=\frac{9}{4}\int_{0}^{4}(4-h)^2dh[/maths]

[maths]=48[/maths]

 

[Affinity]

why bother integrating when we know it is Ah/3

 

[jet]

Cause its never that simple in 4 unit.

 

[cutemouse]

The volume is just a square pyramid height 4m and base 6m by 6m. Slicing the pyramid parallel to base gives square slices of side s and width dh with h being height of slice above base.

By using similar triangles,

[maths]\frac{s/2}{3}=\frac{4-h}{4}[/maths]

Hi, where did you get the 3 and 4's in the denominator from?

Thanks

 

[azureus88]

Heres a diagram

 

[leenayeager]

Hi, does anyone know why the formatting is all weird? The answers aren't in fractions or anything, theyre just shown as weird words. Thank you for the answers by the way!

 

[InteGrand]

Hi, does anyone know why the formatting is all weird? The answers aren't in fractions or anything, theyre just shown as weird words. Thank you for the answers by the way!

Maybe the way LaTeX is used on this site has changed over the years.

 

[InteGrand]

Here is their solution with LaTeX:

The volume is just a square pyramid height 4m and base 6m by 6m. Slicing the pyramid parallel to base gives square slices of side s and width dh with h being height of slice above base.

By using similar triangles,

 

[stupid_girl]

why bother integrating when we know it is Ah/3

It is not necessarily a pyramid. It may have different tilt/twist at different level.
I think integration is the way to go.