Answer :
To find the total volume of the grain silo, which is composed of a cylinder and a hemisphere, we need to calculate the volume of each part and then add them together.
1. Determine the radius:
- The diameter of the silo is given as 4.4 meters. The radius (r) is half of the diameter.
[tex]\[
r = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
2. Calculate the volume of the cylindrical portion:
- The formula for the volume of a cylinder is [tex]\( \pi r^2 h \)[/tex], where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylinder.
- Substitute the values: radius [tex]\( r = 2.2 \)[/tex] meters, height [tex]\( h = 6.2 \)[/tex] meters, and [tex]\( \pi \approx 3.14 \)[/tex].
[tex]\[
\text{Cylinder Volume} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
= approximately 94.2 cubic meters.
3. Calculate the volume of the hemispherical portion:
- The formula for the volume of a hemisphere is [tex]\( \frac{2}{3} \pi r^3 \)[/tex].
- Substitute the values: radius [tex]\( r = 2.2 \)[/tex] meters.
[tex]\[
\text{Hemisphere Volume} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
= approximately 22.3 cubic meters.
4. Find the total volume of the silo:
- Add the volume of the cylindrical portion and the volume of the hemispherical portion.
[tex]\[
\text{Total Volume} = 94.2 + 22.3
\][/tex]
= approximately 116.5 cubic meters.
Thus, the approximate total volume of the silo is 116.5 cubic meters.
1. Determine the radius:
- The diameter of the silo is given as 4.4 meters. The radius (r) is half of the diameter.
[tex]\[
r = \frac{4.4}{2} = 2.2 \text{ meters}
\][/tex]
2. Calculate the volume of the cylindrical portion:
- The formula for the volume of a cylinder is [tex]\( \pi r^2 h \)[/tex], where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylinder.
- Substitute the values: radius [tex]\( r = 2.2 \)[/tex] meters, height [tex]\( h = 6.2 \)[/tex] meters, and [tex]\( \pi \approx 3.14 \)[/tex].
[tex]\[
\text{Cylinder Volume} = 3.14 \times (2.2)^2 \times 6.2
\][/tex]
= approximately 94.2 cubic meters.
3. Calculate the volume of the hemispherical portion:
- The formula for the volume of a hemisphere is [tex]\( \frac{2}{3} \pi r^3 \)[/tex].
- Substitute the values: radius [tex]\( r = 2.2 \)[/tex] meters.
[tex]\[
\text{Hemisphere Volume} = \frac{2}{3} \times 3.14 \times (2.2)^3
\][/tex]
= approximately 22.3 cubic meters.
4. Find the total volume of the silo:
- Add the volume of the cylindrical portion and the volume of the hemispherical portion.
[tex]\[
\text{Total Volume} = 94.2 + 22.3
\][/tex]
= approximately 116.5 cubic meters.
Thus, the approximate total volume of the silo is 116.5 cubic meters.
