Which of the following is not true?
A. In a solid of revolution, the cross-sections are circles or washers.
B. You can figure the volume of a solid by slicing it into cross-
sections, figuring the individual volumes, and adding them up.
C. You can figure the exact volume of a solid by slicing it into cross-
sections, figuring the individual volumes by multiplying cross-
sectional area times thickness, and adding them up.
D. A solid of revolution is obtained by revolving a region about a line.
E. Figuring the volume of a solid can involve slicing it into cross-
sections.
Answer C (Apex)
It is C, I confirm.
E. Figuring the volume of a solid can involve slicing it into cross-sections.
Because in reality, figuring the volume of a solid can definitely involve slicing it into cross-sections. But don't worry, you won't need a knife or any CSI skills for it!
The statement that is not true is:
C. You can figure the exact volume of a solid by slicing it into cross-sections, figuring the individual volumes by multiplying cross-sectional area times thickness, and adding them up.
To determine which of the following statements is not true, let's examine each statement one by one:
A. In a solid of revolution, the cross-sections are circles or washers.
This statement is true. When a region is revolved around a line to form a solid of revolution, its cross-sections are indeed circles or washers, depending on the shape of the original region.
B. You can figure the volume of a solid by slicing it into cross-sections, figuring the individual volumes, and adding them up.
This statement is true. The method described here is commonly known as the "method of slicing." By dividing the solid into thin slices or cross-sections, calculating the volume of each slice, and summing them up, you can find the total volume of the solid.
C. You can figure the exact volume of a solid by slicing it into cross-sections, figuring the individual volumes by multiplying cross-sectional area times thickness, and adding them up.
This statement is true. When applying the slicing method, to find the volume of each slice, you multiply the cross-sectional area by the thickness of the slice. By summing up these volumes, you can determine the exact volume of the entire solid.
D. A solid of revolution is obtained by revolving a region about a line.
This statement is true. When a region is rotated or revolved around a line, it generates a solid of revolution. This revolution creates new cross-sections while maintaining the same base shape as the original region.
E. Figuring the volume of a solid can involve slicing it into cross-sections.
This statement is true. As mentioned earlier, the method of slicing involves dividing a solid into cross-sections to calculate its volume.
After analyzing all the statements, it appears that all of them are true. Therefore, none of the given statements are not true.