Final Examination in MATH 153 - Part 4

The area bounded by the curve y = x², the x-axis and the line x = 1 is rotated about the x-axis. Determine the volume generated?

• π/2
• π/5
• π/4
• π/3

Find the volume formed by revolving about the y-axis the area in the first quadrant bounded by y = cos x and the two axes?

• 3.586
• 4.112
• 2.125
• 2.984

The area common to parabolas y² = x and x² = y is revolved about the y-axis. Find the volume generated.

• 0.93
• 0.94
• 0.95
• 0.96

Find the volume of the solid form by rotating the area bounded by the curves 𝑦 = x² + 1 , the x-axis from x = 0 to x = 2 about the line x = -2.

• 94 π/3
• 95 π/4
• 92 π/3
• 90 π

Find the surface area generated by revolving a rectangle of side 4 cm x 3 cm about the 4 cm side.

• 41 pi
• 40 pi
• 42 pi
• 35 pi

Determine the volume generated by rotating an equilateral triangle of side measuring 10 cm each about one of its side.

• 230 pi
• 250 pi
• 240 pi
• 260 pi

Find the volume of the solid generated by revolving the curve x² + y² – 4x – 6y – 12 = 0 about the line 3x +4y – 48 = 0

• 150π²
• 300π²
• 450π²
• 200π²

Find the moment of inertia of a triangle having base and altitude of 10cm and 16.2 cm respectively.

• 1282 cm⁴
• 1181 cm⁴
• 1350 cm⁴
• 2216 cm⁴

A 60 m cable that weighs 4 kg/m has a 500 kg weight attached at the end. How much work is done in winding up the last 20 m of the cable?

• 12,000 kg - m
• 10,800 kg - m
• 10,000 kg - m
• 11,200 kg - m

A 5-lb monkey is to climb a 20 ft hanging rope that weighs 0.3 lb/ft. If the monkey climbs up to the top at the same time carrying the rope, how much work has it done?

• 160 ft-lb
• 220 ft-lb
• 340 ft-lb
• 180 ft-lb