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Answer :
* Calculates the radius of the silo using the diameter: $r = 4.4 / 2 = 2.2$ m.
* Computes the volume of the cylindrical portion: $V_{cylinder} = \pi r^2 h = 3.14 \times (2.2)^2 \times 6.2 \approx 94.15 m^3$.
* Computes the volume of the hemispherical portion: $V_{hemisphere} = (2/3) \pi r^3 = (2/3) \times 3.14 \times (2.2)^3 \approx 22.35 m^3$.
* Determines the total volume by summing the two volumes: $V_{total} = V_{cylinder} + V_{hemisphere} \approx 116.5 m^3$. The final answer is $\boxed{116.5 m^3}$
### Explanation
1. Problem Analysis and Given Data
The grain silo consists of a cylinder and a hemisphere. We need to find the total volume of the silo by summing the volumes of these two parts. The diameter of the silo is 4.4 meters, so the radius is half of that, which is 2.2 meters. The height of the cylindrical part is 6.2 meters. We'll use 3.14 as the value for $\pi$.
2. Volume of the Cylinder
First, let's calculate the volume of the cylindrical part of the silo. The formula for the volume of a cylinder is $V_{cylinder} = \pi r^2 h$, where $r$ is the radius and $h$ is the height. In our case, $r = 2.2$ meters and $h = 6.2$ meters. So, $V_{cylinder} = 3.14 \times (2.2)^2 \times 6.2$.
3. Volume of the Hemisphere
Now, let's calculate the volume of the hemispherical part of the silo. The formula for the volume of a sphere is $\frac{4}{3} \pi r^3$, so the volume of a hemisphere is half of that, which is $\frac{2}{3} \pi r^3$. In our case, $r = 2.2$ meters. So, $V_{hemisphere} = \frac{2}{3} \times 3.14 \times (2.2)^3$.
4. Total Volume Calculation
Now, we add the volumes of the cylinder and the hemisphere to find the total volume of the silo: $V_{total} = V_{cylinder} + V_{hemisphere}$. $V_{total} = (3.14 \times (2.2)^2 \times 6.2) + (\frac{2}{3} \times 3.14 \times (2.2)^3)$. Calculating these values, we get $V_{cylinder} \approx 94.15$ cubic meters and $V_{hemisphere} \approx 22.35$ cubic meters. Therefore, $V_{total} \approx 94.15 + 22.35 = 116.5$ cubic meters.
5. Final Answer
The approximate total volume of the silo is 116.5 cubic meters, rounded to the nearest tenth.
### Examples
Understanding the volume of silos is crucial in agriculture for storing grains and other agricultural products. Farmers and agricultural businesses need to accurately calculate silo volumes to manage their storage capacity and inventory effectively. This calculation helps in determining how much grain can be stored, planning for harvests, and managing resources efficiently.
* Computes the volume of the cylindrical portion: $V_{cylinder} = \pi r^2 h = 3.14 \times (2.2)^2 \times 6.2 \approx 94.15 m^3$.
* Computes the volume of the hemispherical portion: $V_{hemisphere} = (2/3) \pi r^3 = (2/3) \times 3.14 \times (2.2)^3 \approx 22.35 m^3$.
* Determines the total volume by summing the two volumes: $V_{total} = V_{cylinder} + V_{hemisphere} \approx 116.5 m^3$. The final answer is $\boxed{116.5 m^3}$
### Explanation
1. Problem Analysis and Given Data
The grain silo consists of a cylinder and a hemisphere. We need to find the total volume of the silo by summing the volumes of these two parts. The diameter of the silo is 4.4 meters, so the radius is half of that, which is 2.2 meters. The height of the cylindrical part is 6.2 meters. We'll use 3.14 as the value for $\pi$.
2. Volume of the Cylinder
First, let's calculate the volume of the cylindrical part of the silo. The formula for the volume of a cylinder is $V_{cylinder} = \pi r^2 h$, where $r$ is the radius and $h$ is the height. In our case, $r = 2.2$ meters and $h = 6.2$ meters. So, $V_{cylinder} = 3.14 \times (2.2)^2 \times 6.2$.
3. Volume of the Hemisphere
Now, let's calculate the volume of the hemispherical part of the silo. The formula for the volume of a sphere is $\frac{4}{3} \pi r^3$, so the volume of a hemisphere is half of that, which is $\frac{2}{3} \pi r^3$. In our case, $r = 2.2$ meters. So, $V_{hemisphere} = \frac{2}{3} \times 3.14 \times (2.2)^3$.
4. Total Volume Calculation
Now, we add the volumes of the cylinder and the hemisphere to find the total volume of the silo: $V_{total} = V_{cylinder} + V_{hemisphere}$. $V_{total} = (3.14 \times (2.2)^2 \times 6.2) + (\frac{2}{3} \times 3.14 \times (2.2)^3)$. Calculating these values, we get $V_{cylinder} \approx 94.15$ cubic meters and $V_{hemisphere} \approx 22.35$ cubic meters. Therefore, $V_{total} \approx 94.15 + 22.35 = 116.5$ cubic meters.
5. Final Answer
The approximate total volume of the silo is 116.5 cubic meters, rounded to the nearest tenth.
### Examples
Understanding the volume of silos is crucial in agriculture for storing grains and other agricultural products. Farmers and agricultural businesses need to accurately calculate silo volumes to manage their storage capacity and inventory effectively. This calculation helps in determining how much grain can be stored, planning for harvests, and managing resources efficiently.
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