Use the image to answer the question.

An illustration shows a horizontal rectangle of height 4 inches with a circle of radius 8 inches attached to its top left and a circle of radius 8 inches attached to its bottom right.

Find the surface area of the net diagram of the right circular cylinder. Use 3.14
for π
.

(1 point)
inches2
Remaining Attempts : 3
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1 answer

To calculate the surface area of the right circular cylinder described in your question, we need to understand its dimensions.

From your description, the cylinder has:

  • A height of 4 inches (the height of the rectangle).
  • A base radius of 8 inches (coming from the circles).

The formula for the surface area \( A \) of a right circular cylinder is given by:

\[ A = 2\pi r^2 + 2\pi rh \]

Where:

  • \( r \) is the radius,
  • \( h \) is the height.

Now, plug in the values:

  • \( r = 8 \) inches,
  • \( h = 4 \) inches,
  • Using \( \pi \approx 3.14 \).
  1. Calculate the area of the two circular bases:

\[ 2\pi r^2 = 2 \times 3.14 \times (8^2) \] \[ = 2 \times 3.14 \times 64 \] \[ = 2 \times 3.14 \times 64 = 402.24 \]

  1. Calculate the lateral surface area:

\[ 2\pi rh = 2 \times 3.14 \times 8 \times 4 \] \[ = 2 \times 3.14 \times 32 \] \[ = 2 \times 100.48 = 200.96 \]

  1. Now, add these two areas together:

\[ A = 402.24 + 200.96 = 603.2 \]

So, the surface area of the net diagram of the right circular cylinder is:

\[ \boxed{603.2} \text{ inches}^2 \]