https://file.aiquickdraw.com/mathbot/file/1726145482912mepydick.jpg

Let's solve this step-by-step.

The formula for the volume \( V \) of a sphere is:

\[
V = \frac{4}{3} \pi r^3
\]

where \( r \) is the radius of the sphere. From the image, we know that the steel ball has a **diameter** of 60 millimeters. 

### Step 1: Calculate the radius
The radius \( r \) is half of the diameter:

\[
r = \frac{d}{2} = \frac{60}{2} = 30 \text{ mm}
\]

### Step 2: Calculate the exact volume (a)
Now, substitute \( r = 30 \) into the formula for the volume:

\[
V = \frac{4}{3} \pi (30)^3
\]

Let's calculate that.

\[
30^3 = 27000
\]

So,

\[
V = \frac{4}{3} \pi \times 27000 = \frac{108000}{3} \pi = 36000 \pi \text{ mm}^3
\]

Thus, the exact volume is:

\[
V = 36000 \pi \text{ mm}^3
\]

### Step 3: Find a 2-decimal-place approximation for the volume (b)
To get a numerical approximation, we'll use \( \pi \approx 3.14159 \):

\[
V \approx 36000 \times 3.14159 = 113097.34 \text{ mm}^3
\]

So, the approximate volume is:

\[
V \approx 113097.34 \text{ mm}^3
\]

Would you like any further clarifications or more details?

Here are five related questions to expand your understanding:
1. How does the volume change if the radius of the sphere doubles?
2. What is the surface area of the sphere with the same radius?
3. How would the volume change if the diameter was given in centimeters instead of millimeters?
4. Can the same formula be used for a hemisphere? If not, how would you modify it?
5. How does the volume formula relate to the formula for the area of a circle?

**Tip:** Always check units when calculating the volume, especially when converting between different units of measurement.

The steel ball is in the shape of a sphere and has a diameter of 60 millimeters. Find the exact volume of the sphere and a 2-decimal-place approximation for the volume.

This page explains how to find the exact volume and a 2-decimal-place approximation for the volume of a sphere with a diameter of 60 millimeters using the formula V = 4/3 π r^3. Includes detailed steps and key geometric concepts.

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