Question

Fill in the blanks!

Volume of a Sphere
The formula for the _, V, of a sphere is given by V = 4/3 pi r ^(3) .
- What is the volume of a sphere with a diameter of 6 mm?

6 mm - d = r/2
If the diameter is 6, cut in half, we get _ for r.

V = 4/3 pi r^(3)
V = 4/3 pi (3)^(3)
V = 4/3 pi (27)
V = (4) (_) pi
V = _ pi mm^(3)

Answer 1

Let's fill in the blanks step by step.

1. The formula for the **volume**, V, of a sphere is given by \( V = \frac{4}{3} \pi r^{3} \).

2. If the diameter is 6 mm, cut in half, we get **3 mm** for r.

Now we can proceed with the volume calculation:

3. \( V = \frac{4}{3} \pi (3)^{3} \)

4. \( V = \frac{4}{3} \pi (27) \)

5. \( V = \frac{4 \times 27}{3} \pi \)

6. \( V = \frac{108}{3} \pi = 36 \pi \)

7. Therefore, \( V = 36 \pi \, \text{mm}^{3} \)

Putting it all together, we have:

- The formula for the **volume**, V, of a sphere is given by \( V = \frac{4}{3} \pi r^{3} \).
- If the diameter is 6 mm, cut in half, we get **3 mm** for r.
- The volume is calculated as \( V = 36 \pi \, \text{mm}^{3} \).