1. Identify the Given Values:

- Radius (\( r \)) = 12 mm
- Approximation for \( \pi \) = 3.14

2. Substitute the Values Into the Formula:

\[
V = (4)/(3) * 3.14 * (12)^3
\]

3. Calculate \( 12^3 \) (12 cubed):

\[
12^3 = 12 * 12 * 12 = 1728
\]

4. Plug the Values into the Formula:

\[
V = (4)/(3) * 3.14 * 1728
\]

5. Multiply the Values:

- First, calculate the multiplication: \( 4 * 3.14 * 1728 \)

\[
4 * 1728 = 6912
\]

\[
6912 * 3.14 = 21727.68
\]

6. Divide by 3:

\[
(21727.68)/(3) \approx 7234.56
\]

7. Round to the Nearest Hundredth:

- The volume of the chocolate truffle, rounded to the nearest hundredth, is 7234.56 mm\(^3\).

Therefore, the amount of chocolate in the spherical truffle is approximately 7234.56 mm\(^3\).

1 answer

Your calculations for the volume of the spherical chocolate truffle are generally correct, but let’s reorganize and verify the computation step-by-step:

  1. Identify the Given Values:

    • Radius (\( r \)) = 12 mm
    • Approximation for \( \pi \) = 3.14
  2. Substitute the Values Into the Formula for Volume of a Sphere:

    The formula for the volume \( V \) of a sphere is given by:

    \[ V = \frac{4}{3} \pi r^3 \]

    Substituting the known values:

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

  3. Calculate \( 12^3 \) (12 cubed):

    \[ 12^3 = 12 * 12 * 12 = 1728 \]

  4. Plug the Values into the Formula:

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

  5. Multiply the Values:

    • Start by calculating \( 4 * 1728 \):

    \[ 4 * 1728 = 6912 \]

    • Next, multiply \( 6912 * 3.14 \):

    \[ 6912 * 3.14 = 21727.68 \]

  6. Divide by 3:

    Now, divide \( 21727.68 \) by 3 to finalize the volume:

    \[ V = \frac{21727.68}{3} \approx 7242.56 \]

  7. Round to the Nearest Hundredth:

    The volume of the chocolate truffle, rounded to the nearest hundredth, is approximately 7242.56 mm³.

Therefore, the amount of chocolate in the spherical truffle is approximately 7242.56 mm³.

Your initial rounding step was not accurate; the correct final answer is 7242.56 mm³.