Answer :
Sure! Let’s solve the problem of finding the volume of a cone with a base diameter of 8 cm and a height of 12 cm using the value 3.14 for π.
1. Understand the problem statement:
- We have a cone with a base diameter of 8 cm.
- The height of the cone is 12 cm.
2. Formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where [tex]\( V \)[/tex] is the volume of the cone, [tex]\( r \)[/tex] is the radius of the cone's base, [tex]\( h \)[/tex] is the height of the cone, and [tex]\( \pi \)[/tex] (pi) is approximately 3.14.
3. Find the radius of the base:
The diameter of the base is 8 cm, so the radius ([tex]\( r \)[/tex]) can be calculated as half the diameter:
[tex]\[ r = \frac{\text{diameter}}{2} = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm} \][/tex]
4. Calculate the volume of the cone:
Substitute the values [tex]\( r = 4 \, \text{cm} \)[/tex], [tex]\( h = 12 \, \text{cm} \)[/tex], and [tex]\( \pi = 3.14 \)[/tex] into the volume formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.14 \times (4 \, \text{cm})^2 \times 12 \, \text{cm} \][/tex]
5. Simplify the expression step by step:
[tex]\[ (4 \, \text{cm})^2 = 16 \, \text{cm}^2 \][/tex]
[tex]\[ \frac{1}{3} \times 3.14 \times 16 \, \text{cm}^2 \times 12 \, \text{cm} \][/tex]
6. Perform the multiplication:
[tex]\[ = \frac{1}{3} \times 3.14 \times 16 \times 12 \, \text{cm}^3 \][/tex]
[tex]\[ = \frac{1}{3} \times 3.14 \times 192 \, \text{cm}^3 \][/tex]
[tex]\[ = \frac{1}{3} \times 602.88 \, \text{cm}^3 \][/tex]
[tex]\[ = 200.96 \, \text{cm}^3 \][/tex]
Thus, the volume of the cone is [tex]\( 200.96 \, \text{cm}^3 \)[/tex].
1. Understand the problem statement:
- We have a cone with a base diameter of 8 cm.
- The height of the cone is 12 cm.
2. Formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where [tex]\( V \)[/tex] is the volume of the cone, [tex]\( r \)[/tex] is the radius of the cone's base, [tex]\( h \)[/tex] is the height of the cone, and [tex]\( \pi \)[/tex] (pi) is approximately 3.14.
3. Find the radius of the base:
The diameter of the base is 8 cm, so the radius ([tex]\( r \)[/tex]) can be calculated as half the diameter:
[tex]\[ r = \frac{\text{diameter}}{2} = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm} \][/tex]
4. Calculate the volume of the cone:
Substitute the values [tex]\( r = 4 \, \text{cm} \)[/tex], [tex]\( h = 12 \, \text{cm} \)[/tex], and [tex]\( \pi = 3.14 \)[/tex] into the volume formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.14 \times (4 \, \text{cm})^2 \times 12 \, \text{cm} \][/tex]
5. Simplify the expression step by step:
[tex]\[ (4 \, \text{cm})^2 = 16 \, \text{cm}^2 \][/tex]
[tex]\[ \frac{1}{3} \times 3.14 \times 16 \, \text{cm}^2 \times 12 \, \text{cm} \][/tex]
6. Perform the multiplication:
[tex]\[ = \frac{1}{3} \times 3.14 \times 16 \times 12 \, \text{cm}^3 \][/tex]
[tex]\[ = \frac{1}{3} \times 3.14 \times 192 \, \text{cm}^3 \][/tex]
[tex]\[ = \frac{1}{3} \times 602.88 \, \text{cm}^3 \][/tex]
[tex]\[ = 200.96 \, \text{cm}^3 \][/tex]
Thus, the volume of the cone is [tex]\( 200.96 \, \text{cm}^3 \)[/tex].
