Answer to Question #199572 in Calculus for VPM

Question

You are looking at producing a 3D model of a solid shape you want to manufacture. The shape is a cone which is bounded by the line 𝑦=1/2𝑥 rotated about the 𝑥−𝑎𝑥𝑖𝑠 between 𝑥=0 𝑎𝑛𝑑 𝑥=5?

Use calculus to find its volume.

Answer 1

Solution

$V=\pi\int_{0}^{5}{y^2dx}=\pi\int_{0}^{5}[x/2]^2dx =\frac{π}{4} \frac{x^3}{3}|_0^5=125π/12 = 32.725$