What you’ll learn
Analyze 2D cross-sections.
Key idea
A base-parallel cylinder section is a circle with the same radius as the base.
A circular 2D section uses area and square units, not circumference or 3D volume.
Worked example
Enter the exact value or ordered values in the format requested below.
A right circular cylinder has height 7; a horizontal plane parallel to its bases cuts at height 7/4 above the base. Its cylinder radius is 3. Find exact 2D section area in square units as a multiple of pi, without a unit suffix.
- The cut is strictly between the bases and makes a circle congruent to the base.
- Area=pi*3^2=9π square units.
Answer: 9π
Quick Check
Evaluate a worked attempt at analyze 2d cross-sections, identify the first invalid step, and provide the correction.
A right circular cylinder has height 3; a horizontal plane parallel to its bases cuts at height 3/2 above the base. Radius is 5. Step 1 identifies a circular section of radius 5. Step 2 calls circumference 10π its area. Locate and repair the first invalid step.