Answer
(a) $31.4$ cm.
(b) $5$ cm
(c) $3.32$ cm
(d) $86.8cm^3$
Work Step by Step
(a) The circumference C of the opening of the cup is the same as the arc length for angle $\theta$,
thus $C=6\theta=6\times\frac{5\pi}{3}=10\pi\approx31.4$ cm.
(b) With $C=2\pi r=10\pi$ (use result from (a)), we get $r=5$ cm
(c) Use the Pythagorean Theorem, we have $h^2+r^2=6^2$, with $r=5$ we have
$h^2=36-25=11$ so that $h=\sqrt {11}\approx3.32$ cm
(d) The volume of the cup $V$ is given by $V=\frac{1}{3}\pi r^2h=\frac{\pi}{3}\times5^2\times3.32\approx86.8cm^3$
