Question

point) A tank in the shape of an inverted right circular cone has height 5 meters and radius 4 meters. It is filled with 4 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is δ=1080 kg/m3. Your answer must include the correct units.

Answer 1

Answer:

W = 907963.50 J = 907.96 J

Explanation:

Note: Refer to the figure attached

Now, from the figure we have similar triangles ΔAOB and ΔCOD

we have

$\frac{5}{4}=\frac{x}{r}$

or

$r=\frac{4x}{5}$

Now, the work done to empty the tank can be given as:

$W = \int\limits^4_0 {(5-x)\rho\times g A} \, dx$

or

$W = \int\limits^4_0 {(5-x)1080\times 9.8 (\pi r^2)} \, dx$

or

$W = \int\limits^4_0 {(5-x)\times10584\times (\pi (\frac{4x}{5})^2)} \, dx$

or

$W = 6773.76\pi\int\limits^4_0 {(5-x)x^2)} \, dx$

or

$W = 6773.76\pi[\frac{5}{3}x^3-\frac{1}{4}x^4]^4_0$

or

$W = 6773.76\pi[\frac{128}{3}]$

or

W = 907963.50 J = 907.96 J