Question
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\(^3\).
- 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\(^3\).
Answers
GPT-4o mini
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**.
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**.