To find the volume of a conical perfume bottle, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.
Given:
- Radius \( r = 3.9 \) cm,
- Height \( h = 5.4 \) cm.
Now, plug in the values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (3.9)^2 \times 5.4 \]
First, calculate \( (3.9)^2 \):
\[ (3.9)^2 = 15.21 \]
Now substitute this value back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 15.21 \times 5.4 \]
Next, calculate \( 3.14 \times 15.21 \):
\[ 3.14 \times 15.21 \approx 47.7044 \]
Now use this to calculate the volume:
\[ V = \frac{1}{3} \times 47.7044 \times 5.4 \]
Calculate \( 47.7044 \times 5.4 \):
\[ 47.7044 \times 5.4 \approx 257.99976 \]
Now take \( \frac{1}{3} \) of this product:
\[ V \approx \frac{257.99976}{3} \approx 85.99992 \]
Approximately, this number rounds to:
\[ V \approx 86.0 \text{ cubic centimeters} \]
Thus, the closest answer is:
B. 85.97 cubic centimeters.