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:
\(\[
V = \frac{1}{3} \pi r^2 h
\]\)
where \(\( V \)\) is the volume of the cone, \(\( r \)\) is the radius of the cone's base, \(\( h \)\) is the height of the cone, and \(\( \pi \)\) (pi) is approximately 3.14.
3. Find the radius of the base:
The diameter of the base is 8 cm, so the radius (\(\( r \)\)) can be calculated as half the diameter:
\(\[
r = \frac{\text{diameter}}{2} = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm}
\]\)
4. Calculate the volume of the cone:
Substitute the values \(\( r = 4 \, \text{cm} \)\), \(\( h = 12 \, \text{cm} \)\), and \(\( \pi = 3.14 \)\) into the volume formula:
\(\[
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.14 \times (4 \, \text{cm})^2 \times 12 \, \text{cm}
\]\)
5. Simplify the expression step by step:
\(\[
(4 \, \text{cm})^2 = 16 \, \text{cm}^2
\]\)
\(\[
\frac{1}{3} \times 3.14 \times 16 \, \text{cm}^2 \times 12 \, \text{cm}
\]\)
6. Perform the multiplication:
\(\[
= \frac{1}{3} \times 3.14 \times 16 \times 12 \, \text{cm}^3
\]\)
\(\[
= \frac{1}{3} \times 3.14 \times 192 \, \text{cm}^3
\]\)
\(\[
= \frac{1}{3} \times 602.88 \, \text{cm}^3
\]\)
\(\[
= 200.96 \, \text{cm}^3
\]\)
Thus, the volume of the cone is \(\( 200.96 \, \text{cm}^3 \)\).
