KurilooStudy·Practice·Succeed
Aptitude Topics

Cylinder & Cone

Cylinders and cones feature curved surfaces. Cylinders maintain a uniform circular profile throughout, while cones taper down to a single point.

Fundamental Principles

Cylinder Space Metrics

Volume = $\pi r^2 h$. Curved Surface Area (CSA) tracking just the pipe wall is $2\pi rh$. Total Surface Area (TSA) adding both caps is $2\pi rh + 2\pi r^2$.

Cone Space Metrics

Volume is exactly one-third of a matching cylinder: $V = (1/3)\pi r^2 h$. Curved Surface Area = $\pi rl$, where l is the slant height line.

Essential Formulation Tips

  • Slant height (l) represents the angled line stretching down the side of a cone. It forms a right triangle with the vertical height (h) and radius (r): $l = \sqrt{r^2 + h^2}$.
  • When a question asks about painting or wrapping a pipe, calculate the Curved Surface Area (CSA) and skip the open end caps.

Shortcut Execution Techniques

  • Cylinder to Cone Conversion: If a solid metal cylinder is melted down to forge matching cones with the same radius and height, it will always yield exactly 3 perfect cones.

Contextual Inquiries (FAQs)

Q: What is the difference between vertical height and slant height in a cone?

A: Vertical height (h) is the straight line from the tip down to the center of the circular base. Slant height (l) is the actual distance along the outer angled surface from the tip to the edge of the base.