me m If the cylindrical portion of the silo is 60 meters in height, has a radius of 10 meters and the slant height of each cone is 32 meters, what is the exact surface area of the silo? O 1840 m² 2040 m² O 2240 m² 2440 m²
me m If the cylindrical portion of the silo is 60 meters in height, has a radius of 10 meters and the slant height of each cone is 32 meters, what is the exact surface area of the silo? O 1840 m² 2040 m² O 2240 m² 2440 m²
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
![**Grain Silo Construction and Surface Area Calculation**
One style of grain silo consists of a right cylinder and 2 right cones. One cone is attached to the top of the cylinder and the other is attached to the bottom as shown in Figure 1.
### Diagram Description
- **Figure 1** includes an image of a grain silo and a labeled diagram of the silo.
- The dimensions of the silo are as follows:
- **Cylinder Height**: 60 meters
- **Radius** (R) of both the cylinder and cones: 10 meters
- **Slant Height** (s) of each cone: 32 meters
**Note:** Figure is not drawn to scale.
### Surface Area Calculation
**Question:**
If the cylindrical portion of the silo is 60 meters in height, has a radius of 10 meters, and the slant height of each cone is 32 meters, what is the exact surface area of the silo?
**Options:**
- \( 1840\pi \, \text{m}^2 \)
- \( 2040\pi \, \text{m}^2 \)
- \( 2240\pi \, \text{m}^2 \)
- \( 2440\pi \, \text{m}^2 \)
### Calculation Steps:
1. **Surface area of the cylindrical part:**
\[ \text{Surface Area}_{\text{cyl}} = 2\pi R H \]
\[ = 2\pi \cdot 10 \cdot 60 \]
\[ = 1200\pi \, \text{m}^2 \]
2. **Surface area of one cone:**
\[ \text{Surface Area}_{\text{cone}} = \pi R s \]
\[ = \pi \cdot 10 \cdot 32 \]
\[ = 320\pi \, \text{m}^2 \]
3. **Total surface area of the two cones:**
\[ 2 \times 320\pi \, \text{m}^2 = 640\pi \, \text{m}^2 \]
4. **Total surface area of the silo (excluding the base, which is part of one of the cones):**
\[ \text{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf693007-feb9-4e65-ba86-b1b16e800487%2Fdeba8b53-40aa-4594-af21-f9b139b4ab08%2Fck1kkcq_processed.png&w=3840&q=75)
Transcribed Image Text:**Grain Silo Construction and Surface Area Calculation**
One style of grain silo consists of a right cylinder and 2 right cones. One cone is attached to the top of the cylinder and the other is attached to the bottom as shown in Figure 1.
### Diagram Description
- **Figure 1** includes an image of a grain silo and a labeled diagram of the silo.
- The dimensions of the silo are as follows:
- **Cylinder Height**: 60 meters
- **Radius** (R) of both the cylinder and cones: 10 meters
- **Slant Height** (s) of each cone: 32 meters
**Note:** Figure is not drawn to scale.
### Surface Area Calculation
**Question:**
If the cylindrical portion of the silo is 60 meters in height, has a radius of 10 meters, and the slant height of each cone is 32 meters, what is the exact surface area of the silo?
**Options:**
- \( 1840\pi \, \text{m}^2 \)
- \( 2040\pi \, \text{m}^2 \)
- \( 2240\pi \, \text{m}^2 \)
- \( 2440\pi \, \text{m}^2 \)
### Calculation Steps:
1. **Surface area of the cylindrical part:**
\[ \text{Surface Area}_{\text{cyl}} = 2\pi R H \]
\[ = 2\pi \cdot 10 \cdot 60 \]
\[ = 1200\pi \, \text{m}^2 \]
2. **Surface area of one cone:**
\[ \text{Surface Area}_{\text{cone}} = \pi R s \]
\[ = \pi \cdot 10 \cdot 32 \]
\[ = 320\pi \, \text{m}^2 \]
3. **Total surface area of the two cones:**
\[ 2 \times 320\pi \, \text{m}^2 = 640\pi \, \text{m}^2 \]
4. **Total surface area of the silo (excluding the base, which is part of one of the cones):**
\[ \text{
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