Find the volume of the solid formed by revolving the following curves about the $x$-axis by \(2\pi

Question

Find the volume of the solid formed by revolving the following curves about the $x$-axis by $2\pi$. $y = x^{\frac{3}{2}}, 1 \leq x \leq 4$ $y = \sqrt{25 - x^2}, 0 \leq x \leq 5$ $y = \cos 2x, 0 \leq x \leq \frac{\pi}{4}$ $y = \sec x, 0 \leq x \leq \frac{\pi}{3}$

Accepted Answer

(i) $\frac{255\pi}4$. (ii) $\frac{250\pi}3$. (iii) $\frac{\pi^2}8$. (iv) $\pi\sqrt3$ cubic units.

Volume of revolution about x-axis

Volume of revolution about x-axis

Solution:

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