The equation is .
(a)
Square.
Rewrite the equation is
Area of the squre is
.
Find volume.
The volume of the square is .
Integral limits are and .
Substitute and and .
cubic units.
The volume of the square is .
(b)
Equilateral traingles.
The equilateral triangle width is .
Area of the equilateral triangle is
Substitute in the formula
Find volume.
The volume of the square is .
Integral limits are and .
Substitute and and
cubic units.
The volume of the equilateral triangles is .
(c)
Semicircles:
The semicircle radius is .
Area of the semicircle is
Substitute in the formula
Find volume.
The volume of the square is
Integral limits are and .
Substitute and and .
cubic units.
The volume of the semicircles is .
(d)
Isosceles right triangles:
The isosceles right triangles is
Area of the isosceles right triangles is .
Substitute in the formula.
Find volume.
The volume of the square is
Integral limits are and .
Substitute and and .
cubic units.
The volume of the isosceles right triangles is cubic units.
(a) The volume of the square is cubic units.
(b) The volume of the equilateral triangles is cubic units.
(c) The volume of the semicircles is cubic units.
(d) The volume of the isosceles right triangles is cubic units.
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