Answer
$Volume= \pi (\dfrac{36}{5})$ $cm^3$ and $\space Weight =192 \space g$
Work Step by Step
We integrate the integral to calculate the volume as follows:
$V= \pi \times \int_{0}^{6} (36-x^2) \dfrac{x^2}{144} dx$
Now, $V= \dfrac{ \pi }{144} [12x^3 - \dfrac{x^{5}}{5}]_{0}^{6}$
or, $Volume= \pi (\dfrac{36}{5})$
We are given that $\space density =8.5 \space g/cm^3$
$\space Weight =\pi (\dfrac{36}{5}) \approx 192 \space g$
So, $Volume= \pi (\dfrac{36}{5})$ $cm^3$ and $\space Weight =192 \space g$
