To find the surface area of the net diagram of the right circular cylinder in the given illustration, we first need to understand that the lateral surface area (the curved side) and the areas of the two circular bases need to be accounted for.
Given:
- The height of the cylinder (rectangle) is \( h = 4 \) inches.
- The radius of the circular bases (given by the attached circles) is \( r = 8 \) inches.
Now, the formulas we need are:
- Lateral Surface Area (LSA) of the cylinder: \[ LSA = 2\pi rh \]
- Area of the two circular bases (top and bottom): \[ Area_{bases} = 2 \times \pi r^2 \]
Now we perform the calculations:
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Calculate the Lateral Surface Area: \[ LSA = 2 \times 3.14 \times 8 \times 4 \] \[ LSA = 2 \times 3.14 \times 32 = 6.28 \times 32 = 200.96 , \text{inches}^2 \]
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Calculate the Area of the two circular bases: \[ Area_{bases} = 2 \times (3.14 \times 8^2) \] \[ Area_{bases} = 2 \times (3.14 \times 64) = 2 \times 200.96 = 401.92 , \text{inches}^2 \]
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Total Surface Area (TSA): \[ TSA = LSA + Area_{bases} \] \[ TSA = 200.96 + 401.92 = 602.88 , \text{inches}^2 \]
Thus, the surface area of the net diagram of the right circular cylinder is approximately: \[ \boxed{602.88} , \text{inches}^2 \]