# What is the volume of the solid produced by revolving f ( x ) = 7 &#x2212;<!-- − -->

What is the volume of the solid produced by revolving $f\left(x\right)=7-x,x\in \left[0,2\right]$ around the x-axis?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Jamarcus Shields
y=7-x is a straight line; The volume of revolution is that of a large cone of radius 7 height 7 minus that of smaller cone radius 5 height 5; Using
${V}_{cone}=\frac{1}{3}\pi {r}^{2}h$, Then:
$V=\frac{1}{3}\pi \left(7{\right)}^{2}\left(7\right)-\frac{1}{3}\pi \left(5{\right)}^{2}\left(5\right)$
$=\frac{1}{3}\pi \left({7}^{3}-{5}^{3}\right)$
$=\frac{1}{3}\pi \left(343-125\right)$
$=\frac{218\pi }{3}$
$\approx 228.289$