Answer :
Let's go through each part of the problem step-by-step.
### 3.1.1 Calculate the volume of the cylinder.
To calculate the volume of the cylinder, we use the formula:
[tex]\[ \text{Volume} = \pi r^2 h \][/tex]
Given:
- π (pi) = 3.14
- Radius [tex]\( r \)[/tex] = 6 cm
- Height [tex]\( h \)[/tex] = 12 cm
Substituting the values into the formula:
[tex]\[ \text{Volume} = 3.14 \times (6 \, \text{cm})^2 \times 12 \, \text{cm} \][/tex]
[tex]\[ \text{Volume} = 3.14 \times 36 \, \text{cm}^2 \times 12 \, \text{cm} \][/tex]
[tex]\[ \text{Volume} = 3.14 \times 432 \, \text{cm}^3 \][/tex]
[tex]\[ \text{Volume} = 1356.48 \, \text{cm}^3 \][/tex]
### 3.1.2 Determine the capacity in liters. Round off to one decimal place.
To convert the volume from cubic centimeters to liters, we use the conversion factor [tex]\( 1 \, \text{liter} = 1000 \, \text{cm}^3 \)[/tex].
Given:
- Volume [tex]\( = 1356.48 \, \text{cm}^3 \)[/tex]
Converting to liters:
[tex]\[ \text{Volume in liters} = \frac{1356.48 \, \text{cm}^3}{1000} \][/tex]
[tex]\[ \text{Volume in liters} = 1.35648 \, \text{liters} \][/tex]
And rounding it off to one decimal place:
[tex]\[ \text{Volume in liters (rounded)} = 1.4 \, \text{liters} \][/tex]
### 3.1.3 Draw a simple sketch of the net of a cylinder
A net of a cylinder consists of three parts:
- Two circles (representing the two bases)
- One rectangle (representing the curved surface)
Here is a simple sketch of the net of a cylinder:
```
________
/ \ (Top Circle)
/ \
| |
| | (Curved Surface)
| |
| |
\ /
\________/ (Bottom Circle)
```
### 3.1.4 Find the total surface area of the cylinder.
To find the total surface area of the cylinder, we use the formula:
[tex]\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \][/tex]
Given:
- π (pi) = 3.14
- Radius [tex]\( r \)[/tex] = 6 cm
- Height [tex]\( h \)[/tex] = 12 cm
Substituting the values into the formula:
[tex]\[ \text{Surface Area} = 2 \times 3.14 \times (6 \, \text{cm})^2 + 2 \times 3.14 \times 6 \, \text{cm} \times 12 \, \text{cm} \][/tex]
[tex]\[ \text{Surface Area} = 2 \times 3.14 \times 36 \, \text{cm}^2 + 2 \times 3.14 \times 6 \, \text{cm} \times 12 \, \text{cm} \][/tex]
[tex]\[ \text{Surface Area} = 226.08 \, \text{cm}^2 + 452.16 \, \text{cm}^2 \][/tex]
[tex]\[ \text{Surface Area} = 678.24 \, \text{cm}^2 \][/tex]
So, the total surface area of the cylinder is [tex]\( 678.24 \, \text{cm}^2 \)[/tex].
Summary:
- Volume of the cylinder: [tex]\( 1356.48 \, \text{cm}^3 \)[/tex]
- Capacity in liters (rounded): [tex]\( 1.4 \, \text{liters} \)[/tex]
- Total surface area: [tex]\( 678.24 \, \text{cm}^2 \)[/tex]
### 3.1.1 Calculate the volume of the cylinder.
To calculate the volume of the cylinder, we use the formula:
[tex]\[ \text{Volume} = \pi r^2 h \][/tex]
Given:
- π (pi) = 3.14
- Radius [tex]\( r \)[/tex] = 6 cm
- Height [tex]\( h \)[/tex] = 12 cm
Substituting the values into the formula:
[tex]\[ \text{Volume} = 3.14 \times (6 \, \text{cm})^2 \times 12 \, \text{cm} \][/tex]
[tex]\[ \text{Volume} = 3.14 \times 36 \, \text{cm}^2 \times 12 \, \text{cm} \][/tex]
[tex]\[ \text{Volume} = 3.14 \times 432 \, \text{cm}^3 \][/tex]
[tex]\[ \text{Volume} = 1356.48 \, \text{cm}^3 \][/tex]
### 3.1.2 Determine the capacity in liters. Round off to one decimal place.
To convert the volume from cubic centimeters to liters, we use the conversion factor [tex]\( 1 \, \text{liter} = 1000 \, \text{cm}^3 \)[/tex].
Given:
- Volume [tex]\( = 1356.48 \, \text{cm}^3 \)[/tex]
Converting to liters:
[tex]\[ \text{Volume in liters} = \frac{1356.48 \, \text{cm}^3}{1000} \][/tex]
[tex]\[ \text{Volume in liters} = 1.35648 \, \text{liters} \][/tex]
And rounding it off to one decimal place:
[tex]\[ \text{Volume in liters (rounded)} = 1.4 \, \text{liters} \][/tex]
### 3.1.3 Draw a simple sketch of the net of a cylinder
A net of a cylinder consists of three parts:
- Two circles (representing the two bases)
- One rectangle (representing the curved surface)
Here is a simple sketch of the net of a cylinder:
```
________
/ \ (Top Circle)
/ \
| |
| | (Curved Surface)
| |
| |
\ /
\________/ (Bottom Circle)
```
### 3.1.4 Find the total surface area of the cylinder.
To find the total surface area of the cylinder, we use the formula:
[tex]\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \][/tex]
Given:
- π (pi) = 3.14
- Radius [tex]\( r \)[/tex] = 6 cm
- Height [tex]\( h \)[/tex] = 12 cm
Substituting the values into the formula:
[tex]\[ \text{Surface Area} = 2 \times 3.14 \times (6 \, \text{cm})^2 + 2 \times 3.14 \times 6 \, \text{cm} \times 12 \, \text{cm} \][/tex]
[tex]\[ \text{Surface Area} = 2 \times 3.14 \times 36 \, \text{cm}^2 + 2 \times 3.14 \times 6 \, \text{cm} \times 12 \, \text{cm} \][/tex]
[tex]\[ \text{Surface Area} = 226.08 \, \text{cm}^2 + 452.16 \, \text{cm}^2 \][/tex]
[tex]\[ \text{Surface Area} = 678.24 \, \text{cm}^2 \][/tex]
So, the total surface area of the cylinder is [tex]\( 678.24 \, \text{cm}^2 \)[/tex].
Summary:
- Volume of the cylinder: [tex]\( 1356.48 \, \text{cm}^3 \)[/tex]
- Capacity in liters (rounded): [tex]\( 1.4 \, \text{liters} \)[/tex]
- Total surface area: [tex]\( 678.24 \, \text{cm}^2 \)[/tex]
