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

3 years ago

PLEASE HELP URGENT!!!! Can someone plss help me with these!!

lana66690 [7]

Answer:

ok who are 38 no butplease

4 0

2 years ago

Which step in the construction of copying a line segment ensures that the new line segment has

baherus [9]

Answer:

希 · 斯杰德布德克克贾克什伊索伊菲夫杰杰德克斯克克沃斯克维约沃沃

3 0

2 years ago

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