Since $\rho=\dfrac mV$ (density = mass/volume), we can get the mass/weight of the liquid by integrating the density $\rho(x,y,z)$ over the interior of the tank. This is done with the integral

$\displaystyle\int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{x^2+y^2}^1(2-z^2)\,\mathrm dz\,\mathrm dy\,\mathrm dx$

which is more readily computed in cylindrical coordinates as

$\displaystyle\int_0^{2\pi}\int_0^1\int_{r^2}^1(2-z^2)r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{3\pi}4}$

7 0

2 years ago

Look at the figure. Which point is collinear with points A and C?

sattari [20]

i think its E bc it is on the same line as the other 2 letters

3 0

3 years ago

Read 2 more answers

Work out the circumference of this circle.

tigry1 [53]

C=pid
Since d=9m and pi=3.142, C=3.142*9m=28.278
Rounded to 1 decimal point =28.3

3 0

2 years ago