QuestionFind the volume of the solid obtained by rotating the region in the first quadrant bounded by $$x=0, y=1, x=y^{15}$$ about the line $y=10$.

Studdy Solution
Simplify and calculate the final result:
$$V = 2\pi \left[ \left(\frac{10}{16} - \frac{1}{17}\right) - (0 - 0) \right]$$
$$V = 2\pi \left( \frac{10}{16} - \frac{1}{17} \right)$$
$$V = 2\pi \left( \frac{170}{272} - \frac{16}{272} \right)$$
$$V = 2\pi \left( \frac{154}{272} \right)$$
$$V = 2\pi \left( \frac{77}{136} \right)$$
$$V = \frac{77\pi}{68}$$
The volume of the solid is:
$$\boxed{\frac{77\pi}{68}}$$