Express the total cost C in terms of the height h in meters.

Question

An aquarium with a square base has no top. There is a metal frame. Glass costs 9 dollars/m^2 and the frame costs 5 dollars/m. The volume is to be 20 m^3. Express the total cost C in terms of the height h in meters. (Hint: work out the cost of the glass and frame separately.)

 

Help please? I've tried this multiple times but I'm getting it wrong. 

Answer 1

V = 20 =hb^2. it has a square base, h=height

b^2 =20/h

b=sqr(20/h)

Glass area = b^2 + 4bh = 20/h + 4sqr(20/h)h

metal frame = 8b + 4h = 8sqr(20/h) +4h

cost of glass = 9 x area = 180/h + 36hsqr(20/h)

cost of frame = 5 x length = 20h+ 40sqr(20/h)

total cost = C = 180/h+20h +(36h+40)sqr(20/h)

cost of the glass =