To find the surface area of the net diagram of the right circular cylinder, we need to analyze the dimensions provided in the problem:
- Height of the cylinder (h): Given as 4 inches.
- Radius of the cylinder (r): Given as 8 inches.
The surface area \( A \) of a right circular cylinder can be calculated using the formula:
\[ A = 2\pi r(h + r) \]
Where:
- \( 2\pi r \) is the lateral surface area.
- \( \pi r^2 \) is the area of the top and bottom circular bases (2 of these, hence \(2\pi r^2\)).
Let's calculate it step by step:
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Calculate the lateral surface area: \[ \text{Lateral Surface Area} = 2\pi rh = 2 \times 3.14 \times 8 \times 4 \]
Calculate \( 2 \times 3.14 \): \[ 2 \times 3.14 = 6.28 \]
Then multiply: \[ 6.28 \times 8 = 50.24 \] \[ 50.24 \times 4 = 200.96 \] Thus, the lateral surface area is \( 200.96 \) square inches.
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Calculate the area of the circular bases: \[ \text{Area of one base} = \pi r^2 = 3.14 \times 8^2 \] Calculate \( 8^2 \): \[ 8^2 = 64 \] Then multiply: \[ 3.14 \times 64 = 200.96 \]
The total area for both bases: \[ 2 \times 200.96 = 401.92 \]
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Finally, sum the lateral area and the bases' area: \[ A = \text{Lateral Surface Area} + 2 \times \text{Area of one base} = 200.96 + 401.92 = 602.88 \]
Thus, the total surface area of the right circular cylinder is:
\[ \boxed{602.88 \text{ square inches}} \]