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Sagot :
Answer:
δV/δr,dh = 14.06 cm³
Step-by-step explanation:
The volume of the can is:
Vc = π*r²*h where r is the radius of the base and h is the heigth
If we take partial derivatives for that equation we get:
δV/δr = 2*π*r*h or δV = 2*π*r*h*dr
δV/δh = 2*π*r² or δV = 2*π*r²*dh
Now the can varies its height at the top and the bottom then:
dh = 0.04cm*2 = 0.08 cm
And
dr = 0.04
δV/δr,dh = 2*π*r*h*dr + 2*π*r²*dh
By substitution:
δV/δr,dh = 2*4*6*π*(0.04) + 32*π*(0.08)
δV/δr,dh = 1.92*π + 2.56*π
δV/δr,dh = 14.06 cm³
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