Mathematics: (08.02 mc) a grain silo is shown below: grain silo formed by cylinder with radius 6 feet and height 168 feet and a half sphere on the top what is the volume of grain that could completely fill this silo, rounded to the nearest whole number? use 22 over 7 for pi.

The ratio of trucks to vans should be 3:7...

(08.02 mc) a grain silo is shown below: grain

kristenhani

13.03.2022

19460 cubic feet

Step-by-step explanation:

Since we are given that Grain silo is formed by cylinder and a half sphere on top

We are required to find the volume of grain that could completely fill this silo

Formula of volume of cylinder : $\pi r^{2}h$

Since we are given that the cylinder with which the silo is formed has height 168 feet and radius 6 feet

So, r = 6 feet

h = 168 feet

use π =22/7

Substituting these values in formula

Volume of cylinder $= \frac{22}{7}*(6)^{2} * 168$

$= \frac{22}{7}*36* 168$

$= 19008 feet^{3}$

Thus the volume of cylinder is 19008 cubic feet.

Now since the silo is fomed of half sphere also

Formula of volume of sphere $=\frac{4}{3} \pi r^{3}$

Volume of half sphere $=\frac{\frac{4}{3}}{2} \pi r^{3}$

$=\frac{2}{3} \pi r^{3}$

Since r = 6 feet

So, volume of half sphere $=\frac{2}{3} * \frac{22}{7}*(6)^{3}$

=452.57

Thus the volume of half sphere is 452.57 cubic feet.

Thus the volume of the grain = volume of cylinder +volume of half sphere

=19008+452.57

=19460.57 cubic feet

Hence the volume of grain that could completely fill this silo is 19460 cubic feet ( rounded to the nearest whole number )

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