Find the volume V of the described solid S.

a.The base of S is the triangular region with vertices (0, 0), (4, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles.

b.The base of S is the triangular region with vertices (0, 0), (4, 0), and (0, 4). Cross-sections perpendicular to the x−axis are squares.

c.The base of S is the region enclosed by the parabola y = 5 − 2x2 and the x−axis. Cross-sections perpendicular to the y−axis are squares.

d.The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.

y = −x2 + 14x − 45, y = 0; about the y−axis

a.The base of S is the triangular region with vertices (0, 0), (4, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles.

b.The base of S is the triangular region with vertices (0, 0), (4, 0), and (0, 4). Cross-sections perpendicular to the x−axis are squares.

c.The base of S is the region enclosed by the parabola y = 5 − 2x2 and the x−axis. Cross-sections perpendicular to the y−axis are squares.

d.The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.

y = −x2 + 14x − 45, y = 0; about the y−axis

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