Let's tackle each problem step-by-step.
### Part 3.1: Calculating the Volume of a Cylinder
We need to calculate the volume of a cylinder with the given specifications:
- Diameter = 16 cm
- Height = 6 cm
First, let's determine the radius of the cylinder since the formula requires the radius:
- Radius (r) = Diameter / 2 = 16 cm / 2 = 8 cm
The formula to calculate the volume (V) of a cylinder is:
[tex]\[ V = \pi r^2 h \][/tex]
Substitute the given values into the formula:
[tex]\[ V = 3.14 \times (8 \, \text{cm})^2 \times 6 \, \text{cm} \][/tex]
Now, calculate each step:
1. Square the radius:
[tex]\[ (8 \, \text{cm})^2 = 64 \, \text{cm}^2 \][/tex]
2. Multiply by pi:
[tex]\[ 3.14 \times 64 \, \text{cm}^2 = 200.96 \, \text{cm}^2 \][/tex]
3. Multiply by the height:
[tex]\[ 200.96 \, \text{cm}^2 \times 6 \, \text{cm} = 1205.76 \, \text{cm}^3 \][/tex]
So, the volume of the cylinder is:
[tex]\[ V = 1205.76 \, \text{cm}^3 \][/tex]
### Part 3.2: Determining the Height of the Vaseline Camphor Jar
Given:
- Volume (V) = 400 ml (since 1 ml = 1 cm³, the volume is also 400 cm³)
- Radius (r) = 4 cm
- We need to calculate the height (h)
The formula to calculate the height of a cylinder is:
[tex]\[ h = \frac{V}{\pi r^2} \][/tex]
Substitute the given values into the formula:
[tex]\[ h = \frac{400 \, \text{cm}^3}{3.14 \times (4 \, \text{cm})^2} \][/tex]
Now, calculate each step:
1. Square the radius:
[tex]\[ (4 \, \text{cm})^2 = 16 \, \text{cm}^2 \][/tex]
2. Multiply by pi:
[tex]\[ 3.14 \times 16 \, \text{cm}^2 = 50.24 \, \text{cm}^2 \][/tex]
3. Divide the volume by this product:
[tex]\[ h = \frac{400 \, \text{cm}^3}{50.24 \, \text{cm}^2} = 7.961783439490445 \, \text{cm} \][/tex]
Rounding this to a whole number, we get:
[tex]\[ h \approx 8 \, \text{cm} \][/tex]
So, the height of the Vaseline camphor jar is approximately 8 cm.
