Find a container. Find a glass or vase that will hold liquid. Do not choose a glass with straight edges. The more complicated the shape, the better.

Find the volume using the steps below.

a) Graph your vase. You want to center the base of the vase at the origin so that it is symmetric across the x-axis, and trace half of it in the first quadrant. You need to determine the radius of the glass at regularly spaced height intervals, and generate a table of values. Be precise!

b) Create a piecewise equation to model your vase. You may use the regression function on your calculator to determine the equation. Once you generate your equation, rotate it about the x-axis to generate a solid.

c) Calculate the volume of the solid using the disk method. You may use a calculator to integrate, but show your work.

d) Use a measuring cup to measure the volume and determine the difference between the actual volume and the volume generated using your equation. (Hint: 1 cup = 236.588 cm3; 1 cup = 14.4375 in

What is the error between the true volume and the volume you found with the equation? What might have caused this error in volume? Explain.

e) Calculate the surface area of your vase. You may use a calculator, but show your equations.

Project: Measuring Rotational Volume Step 1: Prepare for the project. Read the entire Student Guide before you begin. If anything is unclear, be sure to ask your teacher for assistance. Step 2: Find a container. Find a glass or vase that will hold liquid. Do not choose a glass with straight edges. The more complicated the shape. the better. Not Complicated Complicated Step 3: Find the volume. a) Graph your vase. You want to center the base of the vase at the origin so that it is symmetric across the xaxis. and trace half of it in the rst quadrant. You need to determine the radius of the glass at regularly spaced height intervals, and generate a table of values. Be precise! Height Radius b) Create a piecewise equation to model your vase. You may use the regression function on your calculator to determine the equation. Once you generate your equation, rotate it about the xaxis to generate a solid. c) Calculate the volume of the solid using the disk method. You may use a calculator to integrate, but show your work. d) Use a measuring cup to measure the volume and determine the difference between the actual volume and the volume generated using your equation. (Hint: 1 cup = 236.588 cma; 1 cup =14.4375 ina) What is the error between the true volume and the volume you found with the equation? What might have caused this error in volume? Explain. 9) Calculate the surface area of your vase. You may use a calculator, but show your equations