Concept explainers
True-False Determine whether the statement is true or false. Explain your answer. [In these exercises, assume that a solid
The average value of
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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_forwardFind the area between the curves in Exercises 1-28. x=0, x=3, y=2e3x, y=e3x+e6arrow_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_forward
- Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed when the region bounded in Quadrant I by the axes and the lines x = 9 and y = 5 is revolved about the a) x-axis b) y-axisarrow_forwardFor the sphers x-12+y+22+z-42=36 and x2+y2+z2=64, find the ratio of their a surface areas. b volumes.arrow_forward
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