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Determine whether each of the following statements is true or false, and explain why.
6. The volume of the solid formed by revolving the function
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Finite Mathematics and Calculus with Applications
- 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_forwardBy expanding (xh)2+(yk)2=r2, we obtain x22hx+h22ky+k2r2=0. When we compare this result to the form x2+y2+Dx+Ey+F=0, we see that D=2h,E=2k, and F=h2+k2r2. Therefore, the center and the length of a radius of a circle can be found by using h=D2,k=E2 and r=h2+k2F. Use these relationship to find the center and the length of the radius of each of the following circles. x2+y2+4x14y+49=0arrow_forward
- Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid right cylinder 9.55 centimeters high contains 1910 cubic centimeters of material. Compute the cross-sectional area of the cylinder.arrow_forwardLet the region R be the area enclosed by the function f(x) = x3 +1 and g(x) = x + 1.Find the volume of the solid generated when the region R is 3 revolved about the line y = 6. You may use a calculator and round to the nearest thousandth. 12 11 10 9 7 -6- 5 4 3 2 X. -2 -1 1 3 4 6. Answer: Submit Answerarrow_forwardConsider the solid object that is obtained when the function: y = 6 (cos(x) - 5) is rotated by 2π radians about the x-axis between the limits x = Find the volume of this object. V = Enter your answer to 3 decimal places. 9π and x = 11πarrow_forward
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