Question

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

1,508.77 cm2
1,508.77 cm squared

1,362.76 cm2
1,362.76 cm squared

1,739.95 cm2
1,739.95 cm squared

4,234.29 cm2

Answer 1

To calculate the surface area of a right circular cylinder, you can use the following formula:

\[
\text{Surface Area} = 2\pi r(h + r)
\]

Where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.

Given:
- Height (\( h \)) = 28 cm
- Diameter = 15.5 cm, so radius \( r = \frac{15.5}{2} = 7.75 \) cm

Now, plug the values into the formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 7.75 \times (28 + 7.75)
\]

Calculating \( h + r \):

\[
h + r = 28 + 7.75 = 35.75 \text{ cm}
\]

Now substitute this value back into the surface area formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 7.75 \times 35.75
\]

First, calculate \( 2 \times 3.14 = 6.28 \).

Then calculate \( 7.75 \times 35.75 \):

\[
7.75 \times 35.75 = 277.5625
\]

Now multiply \( 6.28 \) by \( 277.5625 \):

\[
\text{Surface Area} = 6.28 \times 277.5625 \approx 1742.15625
\]

Round this to two decimal places:

\[
\text{Surface Area} \approx 1742.16 \text{ cm}^2
\]

Given the options, the closest and most accurate choice is:

**1,739.95 cm²**.