$\"\"$

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The equation is $\"\"$ .

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(a)

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Square.

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Rewrite the equation is $\"\"$

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$\"\"$

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Area of the squre is $\"\"$

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$\"\"$

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$\"\"$ .

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Find volume.

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The volume of the square is $\"\"$ .

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Integral limits are $\"\"$ and $\"\"$ .

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Substitute $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ cubic units.

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The volume of the square is $\"\"$ .

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$\"\"$

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(b)

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Equilateral traingles.

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$\"\"$

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The equilateral triangle width is $\"\"$ .

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Area of the equilateral triangle is $\"\"$

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Substitute $\"\"$ in the formula

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$\"\"$

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$\"\"$

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Find volume.

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The volume of the square is $\"\"$ .

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Integral limits are $\"\"$ and $\"\"$ .

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Substitute $\"\"$ and $\"\"$ and $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ cubic units.

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The volume of the equilateral triangles is $\"\"$ .

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$\"\"$

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(c)

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Semicircles:

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$\"\"$

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The semicircle radius is $\"\"$ .

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Area of the semicircle is $\"\"$

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Substitute $\"\"$ in the formula

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$\"\"$

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$\"\"$

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Find volume.

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The volume of the square is $\"\"$

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Integral limits are $\"\"$ and $\"\"$ .

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Substitute $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ cubic units.

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The volume of the semicircles is $\"\"$ .

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$\"\"$

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(d)

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Isosceles right triangles:

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$\"\"$

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The isosceles right triangles is $\"\"$

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Area of the isosceles right triangles is $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in the formula.

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$\"\"$

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$\"\"$

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Find volume.

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The volume of the square is $\"\"$

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Integral limits are $\"\"$ and $\"\"$ .

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Substitute $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ cubic units.

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The volume of the isosceles right triangles is $\"\"$ cubic units.

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$\"\"$

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(a) The volume of the square is $\"\"$ cubic units.

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(b) The volume of the equilateral triangles is $\"\"$ cubic units.

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(c) The volume of the semicircles is $\"\"$ cubic units.

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(d) The volume of the isosceles right triangles is $\"\"$ cubic units.