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 \( \pi \approx 3.14 \).
- Calculate the area of the two circular bases:
\[ 2\pi r^2 = 2 \times 3.14 \times (8^2) \] \[ = 2 \times 3.14 \times 64 \] \[ = 2 \times 3.14 \times 64 = 402.24 \]
- Calculate the lateral surface area:
\[ 2\pi rh = 2 \times 3.14 \times 8 \times 4 \] \[ = 2 \times 3.14 \times 32 \] \[ = 2 \times 100.48 = 200.96 \]
- 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:
\[ \boxed{603.2} \text{ inches}^2 \]