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Question
A coat of paint of thickness 0.2 cm is applied to the faces of cube whose edge is 10 cm. Use the differentials to find approximately how many cubic centimeters of paint is used to paint this cube. Also calculate the exact amount of paint used to paint this cube
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Solution
v = a3
So dv = a2 da
dv (when) a = 10 cm and da = 0.20 cm
= 3(102)(0.2)
= 300 × 0.2
= 60 cm3
Actual paint used = v at x + ∆x
= 10.2 and x = 10 cm
= a3 At x + ∆x
= 10.2 and x = 10
= (10.2)3 – (10)
= 61.2 cm3
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