Question

### Gauthmathier5933

Grade 11 · 2021-01-10

Let C represent the piece of the curve y=\sqrt [3]{64-16x^{2}} that lies in the first quadrant. Let S be the region bounded by C and the coordinate axes.

Find the volume generated when S is rotated about the x-axis.

Find the volume generated when S is rotated about the x-axis.

Good Question (122)

Answer

4.8(568) votes

### Gauthmathier5712

Grade 11 · 2021-01-10

Answer

74.310

Explanation

When S is rotated about the x-axis, its volume can be obtained using disks:

\Delta V=\pi R^{2}\Delta x=\pi y^{2}\Delta x

V=\pi \int _{0}^{2}y^{2}\d x=\pi \int _{0}^{2}(\sqrt [3]{64-16x^{2}})^{2}\d x\approx 74.310

\Delta V=\pi R^{2}\Delta x=\pi y^{2}\Delta x

V=\pi \int _{0}^{2}y^{2}\d x=\pi \int _{0}^{2}(\sqrt [3]{64-16x^{2}})^{2}\d x\approx 74.310

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