Sure! Let's work through the given mathematical expression step by step.
We are given the expression:
[tex]\[
\left(\left(\frac{4 \cdot \pi \cdot r^3}{3}\right) \cdot 63,360\right)-0.0164
\][/tex]
### Step 1: Calculate the volume of a sphere
The first part of the expression involves calculating the volume of a sphere with radius [tex]\( r \)[/tex]. The formula for the volume of a sphere is:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
So, we have:
[tex]\[
\frac{4}{3} \pi r^3
\][/tex]
### Step 2: Multiply by 63,360
Next, we take the volume calculated in step 1 and multiply it by 63,360. We can represent this mathematically as:
[tex]\[
\left( \frac{4 \cdot \pi \cdot r^3}{3} \right) \cdot 63,360
\][/tex]
This simplifies to:
[tex]\[
\frac{4 \cdot \pi \cdot r^3 \cdot 63,360}{3}
\][/tex]
Now we combine the constants:
[tex]\[
\frac{4 \cdot \pi \cdot r^3 \cdot 63,360}{3} = \frac{253440 \pi \cdot r^3}{3}
\][/tex]
This can be further simplified to:
[tex]\[
84480 \pi r^3
\][/tex]
### Step 3: Subtract 0.0164
Finally, we subtract 0.0164 from the result obtained in step 2:
[tex]\[
84480 \pi r^3 - 0.0164
\][/tex]
So, the entire expression simplifies to:
[tex]\[
\frac{4 \cdot \pi \cdot r^3}{3} \cdot 63360 - 0.0164 = 265401.747375266 r^3 - 0.0164
\][/tex]
Therefore, the detailed step-by-step solution of the given expression is:
1. Calculate the volume of the sphere: [tex]\(\frac{4}{3} \pi r^3\)[/tex].
2. Multiply the result by 63,360: [tex]\(265401.747375266 r^3\)[/tex].
3. Subtract 0.0164: [tex]\(265401.747375266 r^3 - 0.0164\)[/tex].
This gives us the final result:
[tex]\[
265401.747375266 r^3 - 0.0164
\][/tex]
