Mathematics, 21.02.2020 05:07 xcrysttallx
When the shaded region below is rotated about the x-axis the resulting solid is a circular cone with radius 2 m and height 3 m. Use the disk or shell method to find the volume of this cone
Answers: 1
![V=\int_0^3\pi \cdot \left(\frac{2}{3}x\right)^2\, dx\\\\V=\int_0^3 \pi \frac{4}{9}x^2\, dx\\\\V= \frac{4\pi}{9} \int_0^3 x^2\, dx\\\\V= \frac{4\pi}{9} \left[\frac{x^3}{3}\right]_0^3\, dx\\\\V= \frac{4\pi}{9}\cdot 9\\\\V=4\pi](/tpl/images/0518/8950/910ee.png)
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