To find the volume of a cone, the formula is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.
In this case, you have provided the measurements as:
- The top of the cone (which we will assume is the smaller end) has a diameter of 9 cm, so the radius \( r_1 \) is:
\[ r_1 = \frac{9 , \text{cm}}{2} = 4.5 , \text{cm} \]
- The bottom of the cone appears to have a height of 5 cm from the top to the base.
To calculate the volume of a truncated cone (frustum), we need the height and the two radii (top and bottom). However, only one radius (the top radius of 4.5 cm) and the height (5 cm) have been given.
If we assume this is a simple cone with height 5 cm, then the truncated cone interpretation might not apply. Conversely, if the bottom radius is actually determined by context, we need that measurement.
Let's assume a scenario where the height (h) is indeed 5 cm and only the radius at the top matters for volume calculation, and it follows that we can ignore the other section or make it minimal as it appears in the top portion only.
So, placing those into the original formula for a basic cone:
- Use \( r = 4.5 , \text{cm} \)
- Use \( h = 5 , \text{cm} \)
Now substituting into the volume formula:
\[ V = \frac{1}{3} \cdot 3.14 \cdot (4.5)^2 \cdot 5 \] \[ V = \frac{1}{3} \cdot 3.14 \cdot 20.25 \cdot 5 \] \[ V = \frac{1}{3} \cdot 3.14 \cdot 101.25 \] \[ V = \frac{1}{3} \cdot 317.325 \] \[ V \approx 105.775 \]
Rounding to the nearest tenth, the volume of the cone is approximately:
\[ \boxed{105.8 , \text{cm}^3} \]
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