rates of change qn (1 Viewer)

[blakwidow]

Cambridge year 11 3 unit

page 267 qn 8

A water trough is 10m long, with cross section a right isos. triangle. Show that when the water has depth h cm, its volume is V = 1000h^2 and its surface area A = 2000h

There is a diagram if you have the book please check.

 

[pLuvia]

Simply find the volume of the tough in terms of r and h, then find something that you can have h replace the r, I'm guessing you'll have to use a triangle in order for this to happen. Similarly with the area.

 

[elseany]

this is acutally pretty simple, i saw this question and was stuck i think yyour making the same mistake as me... just rememver 10m = 1000cm

to find the are of the triangle i split it into two halves producing two right isoceles with height h, and since they were isoceles it also had length h. so the area of the two smaller trianges (i.e. area of larger triangle is 2(1/2*h*h) = h^2 cm^2

so then the volume is equal to the area of the triangle times the length, but the area of the triangle is in cm and the length of the body is in m, so we have to fix the units first and the answer comes out as V = 1000*h^2 cm^2

edit; also to find the surface area of an object, you should have learnt in class that you differentiate your expression of volume with respect to the variable its expressed in. in this case u need to find dV/dh

 

[blakwidow]

this is acutally pretty simple, i saw this question and was stuck i think yyour making the same mistake as me... just rememver 10m = 1000cm

im an idiot...