Sure! Let's solve the problem step-by-step.
### Given Information:
1. The height [tex]\( h \)[/tex] of the cylinder is 60 cm.
2. The diameter of the cylinder is 14 cm.
3. When the cylinder is cut vertically, it is divided into two equal halves.
### Step-by-Step Solution:
1. Calculate the radius of the cylinder:
- The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[
r = \frac{d}{2} = \frac{14 \, \text{cm}}{2} = 7 \, \text{cm}
\][/tex]
2. Calculate the volume of the full cylinder:
- The volume [tex]\( V \)[/tex] of a cylinder is given by the formula:
[tex]\[
V = \pi r^2 h
\][/tex]
- Here, [tex]\( r = 7 \, \text{cm} \)[/tex], [tex]\( h = 60 \, \text{cm} \)[/tex], and [tex]\( \pi \approx 3.1416 \)[/tex].
3. Insert the values into the volume formula:
[tex]\[
V = \pi \times (7 \, \text{cm})^2 \times 60 \, \text{cm}
\][/tex]
- Squaring the radius:
[tex]\[
r^2 = (7 \, \text{cm})^2 = 49 \, \text{cm}^2
\][/tex]
- Multiplying by the height:
[tex]\[
r^2 \times h = 49 \, \text{cm}^2 \times 60 \, \text{cm} = 2940 \, \text{cm}^3
\][/tex]
- Multiplying by [tex]\( \pi \)[/tex]:
[tex]\[
V = \pi \times 2940 \, \text{cm}^3 \approx 3.1416 \times 2940 \, \text{cm}^3 \approx 9236.282 \, \text{cm}^3
\][/tex]
4. Divide the volume of the full cylinder by 2 to find the volume of one half:
[tex]\[
\text{Volume of one half} = \frac{9236.282 \, \text{cm}^3}{2} \approx 4618.141 \, \text{cm}^3
\][/tex]
### Final Answer:
The volume of one half of the 60 cm high cylinder with a 14 cm diameter, when cut vertically into two equal halves, is approximately 4618.141 cm³.
