Sure! Let's work through the problem step by step, breaking it down into manageable parts.
We need to evaluate the expression:
[tex]\[ \left(\left(\frac{4 \pi r^3}{3}\right) \cdot 3360 \cdot 0.0164\right) \][/tex]
### Step 1: Calculate the Volume of a Sphere
First, we evaluate the term [tex]\(\frac{4 \pi r^3}{3}\)[/tex].
Let's use the given value of [tex]\( r = 1 \)[/tex]:
[tex]\[
\frac{4 \pi r^3}{3} = \frac{4 \pi (1)^3}{3} = \frac{4 \pi}{3}
\][/tex]
Since [tex]\(\pi\)[/tex] is approximately 3.14159, we plug that into the expression:
[tex]\[
\frac{4 \pi}{3} = \frac{4 \times 3.14159}{3} \approx \frac{12.56636}{3} \approx 4.18879
\][/tex]
So, the value of [tex]\(\frac{4 \pi r^3}{3}\)[/tex] is approximately 4.18879.
### Step 2: Multiplication by 3360
Next, we need to multiply this result by 3360:
[tex]\[
4.18879 \times 3360 = 14065.2704
\][/tex]
### Step 3: Multiplication by 0.0164
Finally, we take the product of 14065.2704 and 0.0164:
[tex]\[
14065.2704 \times 0.0164 \approx 230.8190954445493
\][/tex]
### Final Answer
Thus, the final result of the given expression:
[tex]\[
\left(\left(\frac{4 \pi r^3}{3}\right) \cdot 3360 \cdot 0.0164\right)
\][/tex]
is approximately 230.8191.
