Question
Marina sells candles that are in the shape of cones. She makes a yellow candle that has a diameter of 4 inches and a height of 11 inches. She sells each candle at a price of $0.35 per cubic inch of wax. Which statements about the yellow candle are true? Check all that apply. Use 3.14 for Pi.
The volume of the yellow candle is about 46.05 inches cubed.
The volume of the yellow candle is about 184.21 inches cubed.
The radius of the yellow candle is 2 in.
The radius of the yellow candle is 8 in.
The base area of the yellow candle is about 6.28 inches squared.
The base area of the yellow candle is about 12.56 inches squared.
The price of one yellow candle is about $64.47.
The price of one yellow candle is about $16.12.
The volume of the yellow candle is about 46.05 inches cubed.
The volume of the yellow candle is about 184.21 inches cubed.
The radius of the yellow candle is 2 in.
The radius of the yellow candle is 8 in.
The base area of the yellow candle is about 6.28 inches squared.
The base area of the yellow candle is about 12.56 inches squared.
The price of one yellow candle is about $64.47.
The price of one yellow candle is about $16.12.
Answers
GPT-4o mini
To determine the true statements about the yellow candle, we first need to calculate its volume, radius, base area, and price.
### Step 1: Calculate the Radius
The diameter of the yellow candle is 4 inches, so the radius \( r \) is:
\[
r = \frac{diameter}{2} = \frac{4}{2} = 2 \text{ inches}
\]
### Step 2: Calculate the Base Area
The base area \( A \) of a cone is calculated using the formula:
\[
A = \pi r^2
\]
Substituting in the radius:
\[
A = 3.14 \times (2^2) = 3.14 \times 4 = 12.56 \text{ inches squared}
\]
### Step 3: Calculate the Volume
The volume \( V \) of a cone is calculated using the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
Substituting the radius and height:
\[
V = \frac{1}{3} \times 3.14 \times (2^2) \times 11
\]
\[
V = \frac{1}{3} \times 3.14 \times 4 \times 11
\]
\[
V = \frac{1}{3} \times 3.14 \times 44
\]
\[
V = \frac{138.16}{3} \approx 46.05 \text{ inches cubed}
\]
### Step 4: Calculate the Price
The price of the candle is calculated by multiplying the volume by the price per cubic inch:
\[
\text{Price} = \text{Volume} \times \text{Price per cubic inch}
\]
\[
\text{Price} = 46.05 \times 0.35 \approx 16.12
\]
### Summary of Results
- The volume of the yellow candle is about **46.05 inches cubed** (True).
- The volume of the yellow candle is about 184.21 inches cubed (False).
- The radius of the yellow candle is **2 in** (True).
- The radius of the yellow candle is 8 in (False).
- The base area of the yellow candle is about **12.56 inches squared** (True).
- The base area of the yellow candle is about 6.28 inches squared (False).
- The price of one yellow candle is about 64.47 (False).
- The price of one yellow candle is about **16.12** (True).
### Conclusion
The true statements about the yellow candle are:
- The volume of the yellow candle is about 46.05 inches cubed.
- The radius of the yellow candle is 2 in.
- The base area of the yellow candle is about 12.56 inches squared.
- The price of one yellow candle is about 16.12.
### Step 1: Calculate the Radius
The diameter of the yellow candle is 4 inches, so the radius \( r \) is:
\[
r = \frac{diameter}{2} = \frac{4}{2} = 2 \text{ inches}
\]
### Step 2: Calculate the Base Area
The base area \( A \) of a cone is calculated using the formula:
\[
A = \pi r^2
\]
Substituting in the radius:
\[
A = 3.14 \times (2^2) = 3.14 \times 4 = 12.56 \text{ inches squared}
\]
### Step 3: Calculate the Volume
The volume \( V \) of a cone is calculated using the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
Substituting the radius and height:
\[
V = \frac{1}{3} \times 3.14 \times (2^2) \times 11
\]
\[
V = \frac{1}{3} \times 3.14 \times 4 \times 11
\]
\[
V = \frac{1}{3} \times 3.14 \times 44
\]
\[
V = \frac{138.16}{3} \approx 46.05 \text{ inches cubed}
\]
### Step 4: Calculate the Price
The price of the candle is calculated by multiplying the volume by the price per cubic inch:
\[
\text{Price} = \text{Volume} \times \text{Price per cubic inch}
\]
\[
\text{Price} = 46.05 \times 0.35 \approx 16.12
\]
### Summary of Results
- The volume of the yellow candle is about **46.05 inches cubed** (True).
- The volume of the yellow candle is about 184.21 inches cubed (False).
- The radius of the yellow candle is **2 in** (True).
- The radius of the yellow candle is 8 in (False).
- The base area of the yellow candle is about **12.56 inches squared** (True).
- The base area of the yellow candle is about 6.28 inches squared (False).
- The price of one yellow candle is about 64.47 (False).
- The price of one yellow candle is about **16.12** (True).
### Conclusion
The true statements about the yellow candle are:
- The volume of the yellow candle is about 46.05 inches cubed.
- The radius of the yellow candle is 2 in.
- The base area of the yellow candle is about 12.56 inches squared.
- The price of one yellow candle is about 16.12.