Question
Aleksandr has a roll of paper that is in the shape of a right circular cylinder. It has a height of 28 cm and a diameter of 15.5 cm. Help Aleksandr solve for the surface area. Use 3.14 for π
.(1 point)
Responses
4,234.29 cm2
4,234.29 cm squared
1,362.76 cm2
1,362.76 cm squared
1,739.95 cm2
1,739.95 cm squared
1,508.77 cm2
.(1 point)
Responses
4,234.29 cm2
4,234.29 cm squared
1,362.76 cm2
1,362.76 cm squared
1,739.95 cm2
1,739.95 cm squared
1,508.77 cm2
Answers
GPT-4o mini
To calculate the surface area of a right circular cylinder, we use the formula:
\[
\text{Surface Area} = 2\pi r(h + r)
\]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is a constant (we'll use \( 3.14 \) as given).
Given:
- Diameter = 15.5 cm, therefore, the radius \( r = \frac{15.5}{2} = 7.75 \) cm.
- Height \( h = 28 \) cm.
Now we can plug these values into the formula:
\[
\text{Surface Area} = 2 \times 3.14 \times 7.75 \times (28 + 7.75)
\]
First, calculate \( h + r \):
\[
h + r = 28 + 7.75 = 35.75 \, \text{cm}
\]
Now substitute back into the surface area formula:
\[
\text{Surface Area} = 2 \times 3.14 \times 7.75 \times 35.75
\]
Calculating each step:
1. \( 2 \times 3.14 = 6.28 \)
2. \( 7.75 \times 35.75 = 277.5625 \)
3. Finally, multiply:
\[
\text{Surface Area} = 6.28 \times 277.5625 \approx 1745.085
\]
Rounding to two decimal places:
\[
\text{Surface Area} \approx 1745.09 \, \text{cm}^2
\]
Based on this calculation, none of the provided answer options match the result exactly, but the closest value would typically be required to choose between the provided options; however, if this is a strict mathematical question, then none are valid.
If you made a mistake in providing the dimensions or the values, please double-check, as \( 1745.09 cm^2 \) seems not to be in the options provided.
\[
\text{Surface Area} = 2\pi r(h + r)
\]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is a constant (we'll use \( 3.14 \) as given).
Given:
- Diameter = 15.5 cm, therefore, the radius \( r = \frac{15.5}{2} = 7.75 \) cm.
- Height \( h = 28 \) cm.
Now we can plug these values into the formula:
\[
\text{Surface Area} = 2 \times 3.14 \times 7.75 \times (28 + 7.75)
\]
First, calculate \( h + r \):
\[
h + r = 28 + 7.75 = 35.75 \, \text{cm}
\]
Now substitute back into the surface area formula:
\[
\text{Surface Area} = 2 \times 3.14 \times 7.75 \times 35.75
\]
Calculating each step:
1. \( 2 \times 3.14 = 6.28 \)
2. \( 7.75 \times 35.75 = 277.5625 \)
3. Finally, multiply:
\[
\text{Surface Area} = 6.28 \times 277.5625 \approx 1745.085
\]
Rounding to two decimal places:
\[
\text{Surface Area} \approx 1745.09 \, \text{cm}^2
\]
Based on this calculation, none of the provided answer options match the result exactly, but the closest value would typically be required to choose between the provided options; however, if this is a strict mathematical question, then none are valid.
If you made a mistake in providing the dimensions or the values, please double-check, as \( 1745.09 cm^2 \) seems not to be in the options provided.