An aquarium with a square base has no top. There is a metal frame. Glass costs 5 dollars/m2 and the frame costs 2 dollars/m. The volume is to be 20 m3. Express the total cost? in terms of the height ℎ in meters. (Hint: work out the cost of the glass and frame separately.)

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Mathematics

10 May, 05:24

An aquarium with a square base has no top. There is a metal frame. Glass costs 5 dollars/m2 and the frame costs 2 dollars/m. The volume is to be 20 m3. Express the total cost? in terms of the height ℎ in meters. (Hint: work out the cost of the glass and frame separately.)

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Edgar Flowers · Answer 1

C = 420/h + 400

Step-by-step explanation:

Let s be the side of the square base.

Let h be the height

Volume = s*h

20 = s*h

s = 20/h

Cost of glass is

5 (20/h) + 5 (4 * h*20/h)

= 100/h + 400

Cost of frame is

2*4 (20/h) + 2*4 (20/h)

= 160/h + 160/h

= 320/h

Total cost = C

C = cost of glass + cost of frame

C = 100/h + 400 + 320/h

C = 420/h + 400