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Answer :
We are given that the silo consists of a cylinder with a hemispherical top. The diameter of the silo is 4.4 meters and the height of the cylindrical part is 6.2 meters. The value for [tex]$\pi$[/tex] is given as 3.14.
First, calculate the radius:
[tex]$$
r = \frac{4.4}{2} = 2.2 \text{ m}.
$$[/tex]
Next, find the volume of the cylinder. The formula for the volume of a cylinder is:
[tex]$$
V_{\text{cyl}} = \pi r^2 h,
$$[/tex]
where [tex]$h$[/tex] is the height of the cylinder. Substituting the known values:
[tex]$$
V_{\text{cyl}} = 3.14 \times (2.2)^2 \times 6.2.
$$[/tex]
Then, find the volume of the hemisphere. The volume of a hemisphere is given by:
[tex]$$
V_{\text{hemi}} = \frac{2}{3}\pi r^3.
$$[/tex]
Substitute the value of [tex]$r$[/tex]:
[tex]$$
V_{\text{hemi}} = \frac{2}{3} \times 3.14 \times (2.2)^3.
$$[/tex]
The total volume of the silo is the sum of the two volumes:
[tex]$$
V_{\text{total}} = V_{\text{cyl}} + V_{\text{hemi}}.
$$[/tex]
After performing the calculations, the volume of the cylinder is approximately 94.2251 m[tex]$^3$[/tex], the volume of the hemisphere is approximately 22.2898 m[tex]$^3$[/tex], and the total volume comes out to be:
[tex]$$
V_{\text{total}} \approx 116.5 \text{ m}^3.
$$[/tex]
Thus, the approximate total volume of the silo is [tex]$\boxed{116.5\text{ m}^3}$[/tex].
First, calculate the radius:
[tex]$$
r = \frac{4.4}{2} = 2.2 \text{ m}.
$$[/tex]
Next, find the volume of the cylinder. The formula for the volume of a cylinder is:
[tex]$$
V_{\text{cyl}} = \pi r^2 h,
$$[/tex]
where [tex]$h$[/tex] is the height of the cylinder. Substituting the known values:
[tex]$$
V_{\text{cyl}} = 3.14 \times (2.2)^2 \times 6.2.
$$[/tex]
Then, find the volume of the hemisphere. The volume of a hemisphere is given by:
[tex]$$
V_{\text{hemi}} = \frac{2}{3}\pi r^3.
$$[/tex]
Substitute the value of [tex]$r$[/tex]:
[tex]$$
V_{\text{hemi}} = \frac{2}{3} \times 3.14 \times (2.2)^3.
$$[/tex]
The total volume of the silo is the sum of the two volumes:
[tex]$$
V_{\text{total}} = V_{\text{cyl}} + V_{\text{hemi}}.
$$[/tex]
After performing the calculations, the volume of the cylinder is approximately 94.2251 m[tex]$^3$[/tex], the volume of the hemisphere is approximately 22.2898 m[tex]$^3$[/tex], and the total volume comes out to be:
[tex]$$
V_{\text{total}} \approx 116.5 \text{ m}^3.
$$[/tex]
Thus, the approximate total volume of the silo is [tex]$\boxed{116.5\text{ m}^3}$[/tex].
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