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MATH 152 Activity 4 (Section 7.2-7.4) Directions: Put both your name and your partners name on the answersheet. Use scratch paper for work, meaning only put the answers on the answer sheet. Turn in only ONE answer sheet per pair. Calculators are allowed and you may use your notes and textbook. Failure to follow these instructions will result in a 1 point deduction. Neat handwriting is expected. 1. The base of a solid lies in a triangle formed in the first quadrant by y = −2x + 6. Cross-sections perpendicular to the y-axis are semicircles. Find the volume of the solid. √ y , y = 4 and x = 0 about the 2. Find the volume of the solid obtained by rotating the region bounded by x = 2 y-axis. 3. Find the volume of the solid obtained by rotating the region bounded by y = x2 , y = 0, x = 1, x = 3 about the line x = 4. 4. How much work is done in lifting a 120 pound weight from the floor to a height of 30 inches? 5. When a particle is at a distance x meters from the origin, a force of f (x) = x3 + x + 5 Newtons acts on the object, thus causing the object to move horizontally along the x-axis. How much work is done in moving the object from x = 1 to x = 2? 6. The natural length of a spring is 12 inches. If a force of 20 lbs is required to hold the spring at a length of 15 inches, find the work done in stretching the spring from its natural length to a length of 18 inches. 1