Answer: Think About It Match each integral with the solid whose volume it represents
Chapter 7, Problem 69(choose chapter or problem)
Think About It Match each integral with the solid whose volume it represents, and give the dimensions of each solid.
(a) Right circular cylinder
(b) Ellipsoid
(c) Sphere
(d) Right circular cone
(e) Torus
(i) \(\pi \int_{0}^{h}\left(\frac{r x}{h}\right)^{2} d x\)
(ii) \(\pi \int_{0}^{h} r^{2} d x\)
(iii) \(\pi \int_{-r}^{r}\left(\sqrt{r^{2}-x^{2}}\right)^{2} d x\)
(iv) \(\pi \int_{-b}^{b}\left(a \sqrt{1-\frac{x^{2}}{b^{2}}}\right)^{2} d x\)
(v) \(\pi \int_{-r}^{r}\left[\left(R+\sqrt{r^{2}-x^{2}}\right)^{2}-\left(R-\sqrt{r^{2}-x^{2}}\right)^{2}\right] d x\)
Text Transcription:
pi int_0^h (rx/h)^2 dx
pi int_0^h r^2 dx
pi int_-r^r (sqrt r^2-x^2)^2 dx
pi int_-b^b (a sqrt 1-x^2/b^2)^2 dx
pi int_-r^r [(R+sqrt r^2-x^2)^2 - (R-sqrt r^2-x^2)^2]dx
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