Answer:
The volume of the metal which make up the can = 179.95 cm^3
Step-by-step explanation:
To solve this the can height = 40 cm
The diameter of the can = 16 cm
The thickness of the top of the can = 0.2 cm
The thickness of the sides = 0.05 cm
The outer volume of the cylinder = pi × r^2 × h = pi × (16/2)^2 × 40 = 8042.5 cm^3
However, the cylinder is 0.2 cm thick on top and 0.05 cm thick on the sides hence
Change in volume dV is given by partial differentiation dV/dr = 2×pi×r×h and dV/dh = 2×pi×r^2×dh
Therefore, dV = dr×2×pi×r×h1 + dh×2×pi×r^2 as V is a function of both h and r
Where h1 = the height of cylinder - top of cylinder = 40-0.2×2 = 39.6 cm
Then we have
dV = 0.05×2×pi×8×39.6 + 0.2×2×pi×8^2 = 99.53 cm^3 + 80.42 cm^3 = 179.95 cm^3
Hence the volume of the metal which make up the can = 179.95 cm^3
