---
title: "Tabulated cylinder surface"
subject: "Computer Aided Design"
chapter: 4
key: "semester_4/computer_aided_design:tabulated-cylinder-surface"
source: https://www.bctengineer.com/q/semester_4/computer_aided_design/tabulated-cylinder-surface
site: BCT Engineering
---

# Tabulated cylinder surface

Computer Aided Design · Chapter 4: Representation of Surfaces and Solids

- Asked in: year not given, 4 marks
- Video: [Plane surface, ruled surface, surface of revolution, tabulated cylinder .part .2 cad/cam. #cadcam.](https://www.youtube.com/watch?v=jXIfusToDhM) — EDUCATION KNORR
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/computer_aided_design/tabulated-cylinder-surface
- Whole chapter: https://www.bctengineer.com/md/semester_4/computer_aided_design/chapter-4

## Question

What is a tabulated cylinder? Write its parametric equation. A planar curve is the quarter circle x = 10 cos(u), y = 10 sin(u), z = 0, 0 <= u <= 90 deg. It is translated along the vector L = (0, 0, 25). Find the surface point at u = 30 deg, w = 0.4.

## Short answer

A tabulated cylinder translates a plane curve along a vector: P(u,w) = C(u) + wL. With C(u)=(10cos u, 10sin u, 0) and L=(0,0,25), at u=30°, w=0.4 the point is (8.660, 5.000, 10.0).

## Answer

A **tabulated cylinder** is a surface generated by translating a plane curve (the directrix) along a straight line of fixed direction and finite length (the generator). All generators are parallel. It is the surface produced by an *extrude* feature in solid modelling; if the directrix is a circle and the direction is perpendicular to its plane, a right circular cylinder results.

#### Equation
$$
\mathbf P(u,w)=\mathbf C(u)+w\,\mathbf L,\qquad 0\le u\le1\ (\text{curve parameter}),\ 0\le w\le1
$$

where $\mathbf C(u)$ is the directrix and $\mathbf L$ is the vector giving the direction and length of translation.

#### Numerical
$$
\mathbf P(u,w)=\big(10\cos u,\ 10\sin u,\ 25w\big)
$$

At $u=30^\circ$ and $w=0.4$:

$$
\begin{aligned}
x&=10\cos30^\circ=8.660 \\
y&=10\sin30^\circ=5.000 \\
z&=25(0.4)=10.0
\end{aligned}
$$

The surface is a quarter of a cylinder of radius 10 and height 25, with its curved area $=\tfrac14(2\pi\times10\times25)=392.7$ square units.

**Answer: P(u,w) = C(u) + wL; the point is (8.660, 5.000, 10.0).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is a tabulated cylinder?
   A. A planar curve translated along a fixed straight line
   B. A curve rotated about an axis
   C. Two curves joined
   D. A net of points
   Answer: A. All generators are parallel. (Key point: Definition)

2. Which equation applies?
   A. P = (1-w)C1 + wC2
   B. P = C(u) + wL
   C. P = C(u) x L
   D. P = wC(u)
   Answer: B. Directrix plus w times translation vector. (Key point: Equation)

3. What is the point at u = 30°, w = 0.4?
   A. (5, 8.66, 10)
   B. (8.660, 5.0, 25)
   C. (8.660, 5.000, 10.0)
   D. (8.66, 5, 0.4)
   Answer: C. z = 25(0.4) = 10. (Key point: Point)

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