Final Examination in MATH 214 - Part 3 - v4

Find the area bounded by the parabolas y = 6x - x² and y = x² - 2x. Note: The parabolas intersect at points (0, 0) and (4, 8).

• 44/3 sq. units
• 54/3 sq. units
• 64/3 sq. units
• 74/3 sq. units

Find the volume of the cone generated by revolving about the y-axis the area bounded by the line 2x + y = 2 and the coordinate axis.

• π
• 2π/3
• π/2
• 1

What is the area bounded by the curve x² - 2y = 0 and x² + 2y - 8 = 0?

• 32/3
• 34/7
• 64/3
• 16/3

Find the area bounded by the curves x² + y² = 9 and 4x² + 9y² = 36, on the first quadrant.

• 2π/3
• 3π/4
• π/2
• 3π/2

The area bounded by the curves y² = 12x and x = 3 is revolved about the line x = 3. What is the volume of generated?

• 181
• 183
• 185
• 187

A hemispherical tank of radius 6 ft is filled with water to a depth of 4 ft. Find the work done in pumping the water to the top of the tank.

• 10.5 ft-tons
• 25.1 ft-tons
• 23.4 ft-tons
• 13.5 ft-tons

Find the centroid of the area bounded by the parabola y = x² and the line y = 2x + 3.

• (1, 17/5)
• (2, 17/5)
• (3, 17/5)
• (4, 17/5)