+790 A company that makes accessories for cars needs a container like the one shown at the right to hold touch-up paint. The hemispherical top will be fitted with a brush applicator. The cylindrical part of the container should be 4 inches tall. The volume of the entire container is 13/12 cubic inches. Find the value of x, the radius of the hemisphere.
1.
a. Write a formula for the volume of the cylindrical part of the container.
b. Write a formula for the volume of the hemispherical part of the container.
2. Write an equation to represent the total volume of the container.
3. Write the equation in standard form.
4. Graph the equation with a graphing calculator. Hint: Use a window with x-values from 8 to 5 with a scale of 1, and y-values from 20 to 250
with a scale of 30 to see the general shape of the graph. Sketch the graph. Then focus on the area of the positive root by using a window of 8 to 3 on the x-axis and 20 to 20 on the y-axis. Use Trace to help you find a possible positive root.
5. Verify the root using synthetic substitution. What is the positive root?
6. Use the Quadratic Formula to find approximate values for the other two roots. Explain why these two roots cannot also be solutions to the problem.
