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MATH 1320 : Spring 2014 Lab 1 Name: Lab Instructor : Kurt VanNess Score: Write all your solutions on a separate sheet of paper. On all of the problems draw a picture to help you solve the problem (except maybe problem 6, but feel free to draw one there too)! 1. The base of a solid is a circular disk with radius 3. Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base. [Hint: The answer is 36, but show all work.] 2. Find the volume of the solid given by rotating the region bounded by the curves y = x2 +1, x = 0, x = 2, and y = 0 around the x-axis. 3. Find the volume of the solid resulting from rotating the region bounded by y = and y = 0 about the y-axis. √ x2 − 4, x = 2, x = 5, 4. Using the arc length formula, calculate the length of the curve defined parametrically by y = 2 sin(t), x = 2 cos(t) from t = π4 to t = π. The arc length, s, of a sector of a circle of radius r is given by s = rθ where θ is the angle of the sector. Check your answer using this formula. 5. A machinist has a hemisphere with radius 1cm made out of some alloy metal. Suppose they wish to have a volume of exactly 1.5cm3 of this metal. How big of a hole would they have to bore through the center of the hemisphere to achieve this volume? 6. A steady wind blows a kite due east. The kite’s height above ground from horizontal position x = 50ft 1 (x − 50)3/2 . Find the distance traveled by the kite. to x = 86ft is given by y = 150 − 12 7. Calculate the volume of the solid given by rotating the region enclosed by the curves y = cos(x), x = π −π 2 , x = 2 , and y = 0 about the line y = 2. Page 1 of 1