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

Which expression is the same as 10÷4? 110 of 4 4÷10 110×14 14 of 10

erica [24]

Answer:

1/4 of 10

Step-by-step explanation:

7 0

2 years ago

Ryan has nine 14 ounce of popcorn to repackage and sell at the school fair. A small bag holds 3 ounces. How many small bags can

ira [324]

Ryan can make 42 small bags of popcorn

5 0

2 years ago