Sure, let's calculate the volume of a sphere given the radius and the value for π (pi). Here is a step-by-step solution for the problem:
### Step-by-Step Solution:
1. Understand the Formula:
The formula for the volume [tex]\( V \)[/tex] of a sphere is given by:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
2. Substitute the Given Values:
We are given:
[tex]\[
r = 4.9 \, \text{mm}
\][/tex]
and
[tex]\[
\pi = 3.14
\][/tex]
3. Calculate the Radius Cubed:
First, compute [tex]\( r^3 \)[/tex] (radius cubed):
[tex]\[
r^3 = (4.9)^3 = 4.9 \times 4.9 \times 4.9
\][/tex]
Let's compute step-by-step:
[tex]\[
4.9 \times 4.9 = 24.01
\][/tex]
[tex]\[
24.01 \times 4.9 = 117.649
\][/tex]
Thus,
[tex]\[
r^3 = 117.649
\][/tex]
4. Substitute into the Volume Formula:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
[tex]\[
V = \frac{4}{3} \times 3.14 \times 117.649
\][/tex]
5. Perform the Multiplications:
First, compute the multiplication of the constants:
[tex]\[
\frac{4}{3} \times 3.14 = 4.1866667 \approx 4.19
\][/tex]
Then multiply by [tex]\( r^3 \)[/tex]:
[tex]\[
V = 4.19 \times 117.649 = 492.18731
\][/tex]
6. Round to the Nearest Tenth:
The volume (V) when rounded to the nearest tenth is:
[tex]\[
V \approx 492.2 \, \text{mm}^3
\][/tex]
### Final Answer:
The volume of the sphere is approximately [tex]\( 492.2 \, \text{mm}^3 \)[/tex].
