Answer:
To calculate the rate of gas production, we'll use the given radius of the bubble (0.1 cm) and the value of π (3.14). Here's the step-by-step calculation:
1. Calculate the Volume of One Bubble:
The formula for the volume \( V \) of a sphere is:
\[
V = \frac{4}{3} \pi r^3
\]
where \( r \) is the radius.
Given \( r = 0.1 \) cm and \( \pi = 3.14 \):
\[
V = \frac{4}{3} \times 3.14 \times (0.1)^3
\]
\[
V = \frac{4}{3} \times 3.14 \times 0.001
\]
\[
V = \frac{4}{3} \times 0.00314
\]
\[
V = 0.0041867 \text{ cm}^3
\]
2. Determine the Number of Bubbles per Second at 40 cm:
According to the information, let's assume the table provides the number of bubbles produced per second at 40 cm. For illustration, let's say the table indicates 50 bubbles per second (this number should be adjusted based on the actual data provided).
3. Calculate the Rate of Gas Production:
The rate of gas production is the total volume of gas produced per second.
\[
\text{Rate of gas production} = \text{Volume of one bubble} \times \text{Number of bubbles per second}
\]
Using the assumed data:
\[
\text{Rate of gas production} = 0.0041867 \text{ cm}^3 \times 50 \text{ bubbles/second}
\]
\[
\text{Rate of gas production} = 0.209335 \text{ cm}^3/\text{second}
\]
4. Express the Rate in Standard Form:
To express 0.209335 cm³/second in standard form with three significant figures:
\[
0.209335 \approx 2.09 \times 10^{-1} \text{ cm}^3/\text{second}
\]
Therefore, the rate of gas production at a distance of 40 cm is \( 2.09 \times 10^{-1} \) cm³/second, given the assumed number of bubbles per second. Adjust this calculation based on the actual number of bubbles per second provided in the table.
