In a crayon factory, wax is rolled into cylinders, each of which are exactly $3.6$ inches long, but the radius (in inches) is a Uniform random variable $X$ on the interval $[0.15, 0.17]$. Find the probability that the volume of a crayon exceeds 0.30 cubic inches. Hint: The volume of a cylinder is $πr^2l$ where $r$ is the radius and $l$ is the length
So what I did was $f(r) = 1/.02 = 50$ for $[0.15, 0.17]$
The volume $0.3 = 3.6\pi r^2$ AKA $.0265 = r^2$ AKA $r = .1629$ (approximately) So if $r$ is greater then or equal to $.1629$ we will have the volume of a crayon exceed $0.3$ cubic inches so
$P(r \geq .1629) = \int_{.1629}^{.17}50rdr = .355$ so the probability should be $.355$
but the answer is $.6434$
Where did I go wrong?