To find the amount of chocolate in a spherical chocolate truffle, we will calculate the volume of the sphere using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius.
Given:
- Radius \( r = 12 \) mm
- Using \( \pi \approx 3.14 \)
Now we can plug in the values:
- Calculate \( r^3 \):
\[ r^3 = 12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1728 \text{ mm}^3 \]
- Now substitute \( r^3 \) into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 1728 \]
- Calculate \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.18667 \]
- Now calculate the volume \( V \):
\[ V \approx 4.18667 \times 1728 \]
- Carrying out the multiplication:
\[ V \approx 7205.51456 \text{ mm}^3 \]
Finally, rounding to the nearest hundredth gives:
\[ V \approx 7205.51 \text{ mm}^3 \]
Thus, the volume of chocolate in the spherical chocolate truffle is approximately 7205.51 mm³.
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