https://file.aiquickdraw.com/mathbot/file/1730420422257jdpe473f.jpg

To solve this problem, we need to calculate the volume \( V \) of a sphere using the given diameter \( D = 8.6 \, \text{cm} \).

### Step-by-Step Solution

1. **Formula for the Volume of a Sphere**:
   \[
   V = \frac{4}{3} \pi r^3
   \]
   where \( r \) is the radius of the sphere.

2. **Calculate the Radius**:
   Since the diameter \( D \) is given, we can find the radius \( r \) by dividing the diameter by 2:
   \[
   r = \frac{D}{2} = \frac{8.6 \, \text{cm}}{2} = 4.3 \, \text{cm}
   \]

3. **Substitute Values into the Volume Formula**:
   Using \( \pi \approx 3.14 \):
   \[
   V = \frac{4}{3} \times 3.14 \times (4.3)^3
   \]

4. **Calculate \( 4.3^3 \)**:
   \[
   4.3^3 = 4.3 \times 4.3 \times 4.3 = 79.507
   \]

5. **Calculate the Volume**:
   Substitute \( 79.507 \) for \( r^3 \):
   \[
   V = \frac{4}{3} \times 3.14 \times 79.507
   \]
   \[
   V \approx \frac{4}{3} \times 249.69698
   \]
   \[
   V \approx 332.9293 \, \text{cm}^3
   \]

6. **Round to the Nearest Tenth**:
   \[
   V \approx 332.9 \, \text{cm}^3
   \]

### Final Answer
The volume of the sphere is approximately:
\[
V = 332.9 \, \text{cm}^3
\]

Would you like further details or have any questions?

---

Here are some related questions that might expand your understanding:

1. What would the volume be if the diameter were doubled?
2. How does the formula for the surface area of a sphere compare to the volume formula?
3. What happens to the volume if the radius is halved?
4. Can the volume formula be derived from basic calculus concepts?
5. How does the value of \( \pi \) affect the final volume result?

**Tip:** Remember, for spheres, the volume increases with the cube of the radius, meaning small changes in radius can significantly impact the volume.

The diameter, D, of a sphere is 8.6 cm. Calculate the sphere's volume, V. Use the value 3.14 for π, and round your answer to the nearest tenth. (Do not round any intermediate computations.)

Learn how to find the volume of a sphere with a diameter of 8.6 cm using the formula V = (4/3)πr^3. This example demonstrates step-by-step calculations and rounds the answer to the nearest tenth. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation