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 4,234.29 cm squared

1 answer

To find the surface area of the right circular cylinder, we can use the formula for the surface area \( A \):

\[ A = 2\pi r(h + r) \]

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 the radius \( r = \frac{15.5}{2} = 7.75 \) cm.

Now, substituting the values into the surface area formula:

\[ A = 2 \cdot 3.14 \cdot 7.75 \cdot (28 + 7.75) \]

First, calculate \( 28 + 7.75 \):

\[ 28 + 7.75 = 35.75 \]

Now substitute that back into the formula:

\[ A = 2 \cdot 3.14 \cdot 7.75 \cdot 35.75 \]

Now, calculate it step by step:

  1. Calculate \( 2 \cdot 3.14 = 6.28 \).
  2. Calculate \( 7.75 \cdot 35.75 \):

\[ 7.75 \cdot 35.75 = 277.5625 \]

  1. Now multiply:

\[ A = 6.28 \cdot 277.5625 \]

Calculating that:

\[ A \approx 1740.045 , \text{cm}^2 \]

Rounding to two decimal places, we get:

\[ A \approx 1740.05 , \text{cm}^2 \]

Looking at the answers provided, the closest option is:

1,739.95 cm²

So, the answer is:

1,739.95 cm²