Advanced Placement Calculus 2016 Graphical Numerical Algebraic Fifth Edition Student Edition
5th Edition
ISBN: 9780133311617
Author: Prentice Hall
Publisher: Prentice Hall
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The area formed by given functions and the y-axis is to be rotated about the y-axis by 180 degrees. Determine the volume of the solid formed.
x2 and y =
8 – x2. Set up, do
3. Let R be the region in the first quadrant bounded by the curves y
not evaluate, the integrals to find the volume of the resulting solid generated by rotating the region
R about the specified axis. In each case, sketch the region and show a representative rectangle.
(a) the x-axis.
(c) the line y = 8.
(b) the line x = 3.
(d) the y-axis.
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.arrow_forwardA soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can, and let h denote the height, both in inches. a. Express the total surface area S of the can, using x and h. Note: The total surface area is the area of the top plus the area of the bottom plus the area of the cylinder. b. Using the fact that the total area is 40 square inches, express h in terms of x. c. Express the volume V of the can in terms of x.arrow_forwardA frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is V=13R2H13rh2arrow_forward
- Use any method to find the volume, V, of the solid obtained by rotating the region enclosed by the curves about the given axis. y² = x¯¹, x = 1, (Express numbers in exact form. Use symbolic notation and fractions where needed.) X = 6, axis y = −6 V = (156+24√√6 +ln(6))π Incorrect < Feedback You have not correctly calculated the volume of the solid. Slice the region vertically and use the washer method to find the volume of the solid of revolution. b [*(Router - Riner) dx a V = π X Note that a and b are the x-coordinates of the intersection points. Find Router as the distance from the axis of rotation to the top point of the region. Find Rinner as the distance from the axis of rotation to the bottom point of the region.arrow_forwardPlease explain how to solve, thank you!arrow_forward
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