Chapter 5 - Applications of Integration - 5.2 Volumes - 5.2 Exercises - Page 374: 4

$$ \frac{94\pi}{3}$$

$y=\sqrt{25-x^2}, y=0, x=2,\ \ x=4 ; \quad$ about the $x$-axis Here \begin{aligned} A(x)&= \pi f^2(x)\\ &= \pi (25-x^2) \end{aligned} Then the volume of the solid given by \begin{aligned} V&= \int_a^bA(x)dx\\ &= \pi\int_2^4 (25-x^2)dx\\ &=\pi (25x-\frac{1}{3}x^3)\bigg|_2^4\\ &= \frac{94\pi}{3} \end{aligned}