- #1

Dethrone

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I'm not in the mood to tackle a 3D problem, so let's revert to a 2D problem :D

Suppose you have a (hollow) sphere, made of some metal with radius 21 cm. The metal is 0.05 cm thick. Calculus the amount of metal.

Using differentials, we have $dV=4 \pi r^2 \,dr=4\pi (21)^2(0.05)$

I was thinking...couldn't this problem be also solved this way?

$$\int_r^{r+\Delta r}4\pi r^2 \,dr=\int_{21}^{21.05}4 \pi r^2 \,dr$$

The first method gives me $277.08 \text{ cm}^3$ where as the second gives me $277.75\text{ cm}^3$. Why are they different?