Question

find the volume of the solid whose base is the region bounded by the x-axis, the curves y=5x, y=3x^2, x=0 and x=1.66667 and which has the property that each cross section perpendicular to the x-axis is an equilateral triangle. VOLUME=???

Answer 1

`(1250\pi)/(81)`

Explanation:

Volume of solid of revolution between the curves y=5x and y=3x^2 around x-axis on interval [0, 5/3] can be found by using integral as follows:

`Volume = \int\limits^{(5)/(3)}_0 \pi ((5x)^2-(3x^2)^2)dx=\pi\int\limits^{(5)/(3)}_0(25x^2-9x^4)dx=\\\\=\pi((25)/(3)x^3-(9)/(5)x^5)|^{(5)/(3)}_0=(1250\pi)/(81)`