Maria wants to find the surface area of a steel rod that is in the shape of a right circular cylinder. The diameter is 0.50 inches, and the length is 36 inches. What is the surface area? Use 3.14 for π

.(1 point)
Responses

0.39 inches2
0.39 inches squared

56.91 inches2
56.91 inches squared

114.61 inches2
114.61 inches squared

56.52 inches2
56.52 inches squared

1 answer

To find the surface area of a right circular cylinder, we can use the formula:

\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]

where:

  • \( r \) is the radius of the base of the cylinder,
  • \( h \) is the height (or length) of the cylinder.

First, we need to calculate the radius of the cylinder. The diameter is given as 0.50 inches, so the radius \( r \) is:

\[ r = \frac{\text{diameter}}{2} = \frac{0.50}{2} = 0.25 \text{ inches} \]

The length \( h \) is given as 36 inches.

Now we substitute these values into the surface area formula:

  1. Calculate the area of the two circular bases:

\[ 2\pi r^2 = 2 \times 3.14 \times (0.25)^2 = 2 \times 3.14 \times 0.0625 = 0.3925 \text{ inches}^2 \]

  1. Calculate the lateral surface area:

\[ 2\pi rh = 2 \times 3.14 \times 0.25 \times 36 = 2 \times 3.14 \times 9 = 56.52 \text{ inches}^2 \]

  1. Add both areas together to find the total surface area:

\[ \text{Surface Area} = 0.3925 + 56.52 \approx 56.9125 \text{ inches}^2 \]

Rounding this to two decimal places, we find:

\[ \text{Surface Area} \approx 56.91 \text{ inches}^2 \]

Thus, the correct response is:

56.91 inches² (or 56.91 inches squared)