Question 4. A metal rod 15 cm long and 5 cm in diameter is to be covered (except for the ends) with insulation that is 0.1 cm thick. Use differentials to estimate the volume of insulation.
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The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. In this case, the radius is half of the diameter, so r = 5/2 = 2.5 cm, and the height is 15 cm. Show more…
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A metal rod $15 \mathrm{cm}$ long and $5 \mathrm{cm}$ in diameter is to be covered (except for the ends) with insulation that is $0.001 \mathrm{cm}$ thick. Use differentials to estimate the volume of insulation. IHint: Let $\Delta V$ be the change in volume of the rod. 1
The Derivative
Local Linear Approximation; Differentials
A metal rod $15 \mathrm{~cm}$ long and $5 \mathrm{~cm}$ in diameter is to be covered (except for the ends) with insulation that is $0.1 \mathrm{~cm}$ thick. Use differentials to estimate the volume of insulation. [Hint: Let $\Delta V$ be the change in volume of the rod.]
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