How much chocolate is in a spherical chocolate truffle with a radius of 12 mm? Use 3.14 as an approximation for pi. Round your answer to the nearest hundredth, if necessary!

Answer 1

To find the volume of a spherical chocolate truffle, we can use 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 of the sphere. Given that the radius \( r \) is 12 mm, and using \( \pi \approx 3.14 \), we can plug in the values:

1. Calculate \( r^3 \):

\[ r^3 = 12^3 = 12 \times 12 \times 12 = 1728 , \text{mm}^3 \]

2. Now use the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times 1728 \]

3. Calculate \( \frac{4}{3} \times 3.14 \):

\[ \frac{4}{3} \times 3.14 \approx 4.1867 \]

4. Now multiply this result by 1728:

\[ V \approx 4.1867 \times 1728 \]

Calculating this:

\[ V \approx 7245.8176 , \text{mm}^3 \]

5. Rounding to the nearest hundredth, the volume of the chocolate truffle is:

\[ \boxed{7245.82} , \text{mm}^3 \]