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Answer :
- Calculate the volume of the sphere using the formula: $$V = \frac{4}{3} \pi r^3$$.
- Substitute the given radius $r = 0.2$ meters into the formula.
- Convert the volume from cubic meters to liters by multiplying by 1000.
- The volume of the spherical container is approximately: $\boxed{33.5 \text{ liters}}$.
### Explanation
1. Problem Analysis
The problem asks us to calculate the volume of water, in liters, that can fit inside a spherical glass container with a radius of 0.2 meters.
2. Volume Formula
We will use the formula for the volume of a sphere, which is $$V = \frac{4}{3} \pi r^3$$, where $V$ is the volume and $r$ is the radius of the sphere. In this case, $r = 0.2$ meters.
3. Calculate Volume in Cubic Meters
First, we calculate the volume in cubic meters:
$$V = \frac{4}{3} \pi (0.2)^3 = \frac{4}{3} \pi (0.008) \approx 0.03351
\text{ m}^3$$
4. Convert to Liters
Next, we convert the volume from cubic meters to liters. Since 1 cubic meter is equal to 1000 liters, we multiply the volume in cubic meters by 1000:
$$V \approx 0.03351 \text{ m}^3 \times 1000 \frac{\text{liters}}{\text{m}^3} = 33.51 \text{ liters}$$
5. Final Answer
Comparing our calculated volume to the given options, the closest answer is 33.5 liters.
### Examples
Understanding the volume of spheres is useful in many real-world applications. For example, when designing spherical tanks for storing liquids or gases, engineers need to accurately calculate the volume to ensure the tank meets the required capacity. Similarly, in the pharmaceutical industry, knowing the volume of spherical capsules is crucial for determining the correct dosage of medication. Even in cooking, understanding spherical volumes can help estimate the amount of ingredients needed for recipes involving spherical fruits or desserts.
- Substitute the given radius $r = 0.2$ meters into the formula.
- Convert the volume from cubic meters to liters by multiplying by 1000.
- The volume of the spherical container is approximately: $\boxed{33.5 \text{ liters}}$.
### Explanation
1. Problem Analysis
The problem asks us to calculate the volume of water, in liters, that can fit inside a spherical glass container with a radius of 0.2 meters.
2. Volume Formula
We will use the formula for the volume of a sphere, which is $$V = \frac{4}{3} \pi r^3$$, where $V$ is the volume and $r$ is the radius of the sphere. In this case, $r = 0.2$ meters.
3. Calculate Volume in Cubic Meters
First, we calculate the volume in cubic meters:
$$V = \frac{4}{3} \pi (0.2)^3 = \frac{4}{3} \pi (0.008) \approx 0.03351
\text{ m}^3$$
4. Convert to Liters
Next, we convert the volume from cubic meters to liters. Since 1 cubic meter is equal to 1000 liters, we multiply the volume in cubic meters by 1000:
$$V \approx 0.03351 \text{ m}^3 \times 1000 \frac{\text{liters}}{\text{m}^3} = 33.51 \text{ liters}$$
5. Final Answer
Comparing our calculated volume to the given options, the closest answer is 33.5 liters.
### Examples
Understanding the volume of spheres is useful in many real-world applications. For example, when designing spherical tanks for storing liquids or gases, engineers need to accurately calculate the volume to ensure the tank meets the required capacity. Similarly, in the pharmaceutical industry, knowing the volume of spherical capsules is crucial for determining the correct dosage of medication. Even in cooking, understanding spherical volumes can help estimate the amount of ingredients needed for recipes involving spherical fruits or desserts.
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