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. mm3

1 answer

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, we can plug in the values:

\[ V = \frac{4}{3} \times 3.14 \times (12)^3 \]

First, we calculate \( (12)^3 \):

\[ 12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1728 \]

Now substitute this value back into the volume formula:

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

Calculating \( \frac{4}{3} \times 3.14 \):

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

Now multiply this by 1728:

\[ V \approx 4.1867 \times 1728 \approx 7224.576576 \]

Rounding this to the nearest hundredth gives:

\[ V \approx 7224.58 \text{ mm}^3 \]

Thus, the volume of the spherical chocolate truffle is approximately 7224.58 mm³.