A wooden trunk has length 100cm, width 60cm, and height 50cm. The lateral walls

Question

A wooden trunk has length 100cm, width 60cm, and height 50cm. The lateral walls are 1.5cm thick, the bottom 2.5cm thick, and the lid 2cm thick. The wood has density 0.7g/cm^3 Estimate the mass of the tank using differentials. Hint: introduce notation for each quantity in the problem. A wooden trunk has length 100cm, width 60cm, and height 50cm. The lateral walls are 1.5cm thick, the bottom 2.5cm thick, and the lid 2cm thick. The wood has density 0.7g/cm^3 Estimate the mass of the tank using differentials. Hint: introduce notation for each quantity in the problem. The wood has density 0.7g/cm^3 Estimate the mass of the tank using differentials. Hint: introduce notation for each quantity in the problem.

Explanation / Answer

x = length

y = width

z = height

So, V = xyz

Differentiating :

dV = xy*dz + yz*dx + xz*dy

dV = (100)(60)(4.5) + (60)(50)(1.5) + (100)(50)(1.5)

dV = 39000 cm^3

Actual volume, V = 100*60*50 = 300000 cm^3

Total volume is 339000 cm^3

MAss = 339000 * 0.7

MAss = 237300 g

or 237.3 kilograms -----> ANSWER

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IF this does not work, plz try 39000 * 0.7 = 27300 g

or 27.3 kilograms

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