2019 Paper 2 Question 9 11th Oct 20201st Nov 2020nstmathsupervisor Share this:TweetMore Email a link to a friend (Opens in new window) Email Like Loading... Related
![\begin{aligned}m &= \iiint \rho(r) dV \\ &= \int_{\phi=0}^{2\pi}\int_{\theta=0}^{\pi}\int_{r=0}^{a}(1+r)\, r^2 \sin\theta dr d\theta d\phi\\ &= \int_{\phi=0}^{2\pi} d\phi \int_{\theta=0}^{\pi} \sin\theta d\theta \left[ \frac{r^3}{3}+ \frac{r^4}{4} \right]_0^a \\ &= 4\pi \left( \frac{a^3}{3}+ \frac{a^4}{4} \right) \\ \end{aligned}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Baligned%7Dm+%26%3D+%5Ciiint+%5Crho%28r%29+dV+%5C%5C+%26%3D+%5Cint_%7B%5Cphi%3D0%7D%5E%7B2%5Cpi%7D%5Cint_%7B%5Ctheta%3D0%7D%5E%7B%5Cpi%7D%5Cint_%7Br%3D0%7D%5E%7Ba%7D%281%2Br%29%5C%2C+r%5E2+%5Csin%5Ctheta+dr+d%5Ctheta+d%5Cphi%5C%5C+%26%3D+%5Cint_%7B%5Cphi%3D0%7D%5E%7B2%5Cpi%7D+d%5Cphi+%5Cint_%7B%5Ctheta%3D0%7D%5E%7B%5Cpi%7D+%5Csin%5Ctheta+d%5Ctheta++%5Cleft%5B+%5Cfrac%7Br%5E3%7D%7B3%7D%2B+%5Cfrac%7Br%5E4%7D%7B4%7D+%5Cright%5D_0%5Ea+%5C%5C+%26%3D+4%5Cpi+%5Cleft%28+%5Cfrac%7Ba%5E3%7D%7B3%7D%2B+%5Cfrac%7Ba%5E4%7D%7B4%7D+%5Cright%29+%5C%5C+%5Cend%7Baligned%7D+&bg=ffffff&fg=333A42&s=0&c=20201002)
NST First Year Maths 