To find the approximate inside volume of the cylindrical pipe, we first need to determine the dimensions of the inner cylinder (the hollow part) after accounting for the wall thickness.
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Outer Dimensions:
- Height (h) = 16 inches
- Outer diameter = 6 inches
- Outer radius (R) = Outer diameter / 2 = 6 inches / 2 = 3 inches
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Inner Dimensions:
- The wall thickness is 1.25 inches, so we subtract twice the wall thickness from the outer diameter to find the inner diameter.
- Inner diameter = Outer diameter - 2 × wall thickness = 6 inches - 2 × 1.25 inches = 6 inches - 2.5 inches = 3.5 inches
- Inner radius (r) = Inner diameter / 2 = 3.5 inches / 2 = 1.75 inches
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Calculating Inner Volume: The volume \( V \) of a cylinder is calculated using the formula: \[ V = \pi r^2 h \] where \( r \) is the inner radius and \( h \) is the height.
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Substituting the Values: \[ V = \pi (1.75)^2 (16) \] \[ V = \pi (3.0625) (16) \] \[ V = \pi (48.99999999) \] \[ V \approx 3.14159 \times 49 \approx 154.2 \text{ cubic inches} \]
Therefore, the approximate inside volume of the pipe is 154 cubic inches.
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