$\"\"$

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The diameter of the base, the diagonal, and the lateral

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edge of the cylinder form a right triangle. Use the

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Pythagorean Theorem to find the height.

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$\"\"$ (Pythagorean theorem)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Evaluate powers)

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$\"\"$ (Subtract 64 from each side)

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$\"\"$ (Simplify)

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$\"\"$ (Subtract: $\"\"$ )

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$\"\"$ (Take the square root of each side) $\"\"$

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Given that diameter of a cylinder(d) = 8 inches.

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$\"\"$

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Divide each side by 2)

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$\"\"$ (Cancel common terms)

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$\"\"$ (Divide: $\"\"$ ) $\"\"$

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Volume(V):

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$\"\"$ (Volume of a cylinder)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Evaluate powers)

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$\"\"$ (Multiply: $\"\"$ )

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Multiply: $\"\"$ ) $\"\"$

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The volume is approximately 753.6 cubic inches.