A sphere and a cylinder have the same radius and height. The volume of the cylinder is 54 meters cubed. Amie found the volume of the sphere.

A sphere with height h and radius r. A cylinder with height h and radius r.

Her work is shown below.

V = two-thirds + 54. V = two-thirds + StartFraction 162 Over 3 EndFraction. V = StartFraction 164 Over 3 EndFraction meter cubed.

What is Amie’s error?
Amie should have multiplied 54 by Two-thirds.
Amie should have multiplied 54 by Four-thirds pi.
Amie should have multiplied 54 by Four-thirds.
Amie should have multiplied 54 by Two-thirds pi.

What is the most accurate measurement of 1 pound

The data shown in the table below represents the weight, in pounds, of a little girl, recorded each year on her birthday. age (in years) weight (in pounds) 2 32 6 47 7 51 4 40 5 43 3 38 8 60 1 23 part a: create a scatter plot to represent the data shown above. sketch the line of best fit. label at least three specific points on the graph that the line passes through. also include the correct labels on the x-axis and y-axis. part b: algebraically write the equation of the best fit line in slope-intercept form. include all of your calculations in your final answer. part c: use the equation for the line of best fit to approximate the weight of the little girl at an age of 14 years old.

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.