Question

Find the volume of the solid of revolution formed when the arc of the parabola
y^2= 4ax between x = 0 and x = a is resolved about the x − axis

Answer 1

Answer on Question #84926 – Math – Calculus

Question

Find the volume of the solid of revolution formed when the arc of the parabola $y^2 = 4ax$ between $x = 0$ and $x = a$ is resolved about the $x$-axis.

Solution

$$y = f(x)$$ $$y^2 = f^2(x) = 4ax$$ $$V = \pi \int_{0}^{a} f^2(x) \, dx = \pi \int_{0}^{a} 4a \, dx = 2\pi a x^2 \Big|_{0}^{a} = 2\pi a (a^2 - 0) = 2\pi a^3$$

Answer: $2\pi a^3$.

Answer provided by https://www.AssignmentExpert.com