. Applied calculus; principles and applications . = 47ra= 47ra 2Tr^a¥ = 282 INTEGRAL CALCULUS Note. — The last form of the result shows that the volumeis the product of the area of the cross section and the lengthof the circumference described by the center of the revolvingcircle, radius a being mean of a + 6 and a — b. EXERCISE XXXI. 1. Find the volume of the right conoid whosebase is a circle of radius a, and whose altitudeis h. (a) With origin at 0, on the circumference;y^ = 2ax - x\ (6) With origin at C, center; y^ = a^ — x^. Ans. ^-. 2. An isosceles triangle moves perpendicula
. Applied calculus; principles and applications . = 47ra= 47ra 2Tr^a¥ = 282 INTEGRAL CALCULUS Note. — The last form of the result shows that the volumeis the product of the area of the cross section and the lengthof the circumference described by the center of the revolvingcircle, radius a being mean of a + 6 and a — b. EXERCISE XXXI. 1. Find the volume of the right conoid whosebase is a circle of radius a, and whose altitudeis h. (a) With origin at 0, on the circumference;y^ = 2ax - x\ (6) With origin at C, center; y^ = a^ — x^. Ans. ^-. 2. An isosceles triangle moves perpendicular to the plane of theellipse x^/a^ + y^/V^ = 1, its base is the double ordinate of the ellipse,and the vertical angle 2 A is constant. Find the volume generated bythe triangle. 4 ab^ cot A o X? ifi Z^ 3. Find the volume of the ellipsoid -^+r^ + i = Iby considering the volume generated by moving a variable ellipse along the axis of of ellipse = irab. From result get volume of a sphere. Ans. jTrabc. 4. A football is 16 inches long and a plane section containing a se
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