# VectorPaint cone nets: distinguish slant height, sector arc and base circle

Language: en
Canonical: [VectorPaint cone nets: distinguish slant height, sector arc and base circle](<https://allluckly.cn/en/guides/vectorpaint-cone-sector-net-slant-arc/>)
中文：[中文 HTML](<https://allluckly.cn/guides/vectorpaint-cone-sector-net-slant-arc/>)
English: [English HTML](<https://allluckly.cn/en/guides/vectorpaint-cone-sector-net-slant-arc/>)
Published: 2026-11-09T00:00:00+08:00
Modified: 2026-11-09T09:37:10+08:00
Author: Bison

Calculate a sector angle for an invented right cone, checking its arc against base circumference without using vertical height as the sector radius.

English translation of the [Chinese original](<https://allluckly.cn/guides/vectorpaint-cone-sector-net-slant-arc/>), translated on 2026-11-09. Original publication dates, attribution, code and version notes are retained.

A cylinder unfolds to a rectangle; a cone’s lateral surface requires a sector. Specify a right circular cone, fix base radius and slant height, then calculate the sector angle, using a different rule from cylinder unfolding. VectorPaint supplies manual shapes/labels and external calculations verify geometry, without packaging dies, material-thickness or bonding-precision guarantees.

## Fix base radius and slant height separately

Set base radius60 and slant height150 in exercise units. Slant height follows the side from apex to rim, not vertically to the base centre. Label both separately in the side view. An optional vertical height follows the right-triangle relation, approximately137.477 rather than150. Restrict this to an ideal zero-thickness right cone, excluding oblique cones. A resized form view may serve composition but is not a screen-measurement source for the separately scaled net.

## Use slant height as the sector radius

Mark the net centre as the cone apex and construct a pale radius150 reference circle. The lateral surface is a sector of that circle, not a radius60 sector. Both radial edges are150 and identify the same side seam when rolled. Use available path/shape methods without assuming a cone-unfold command. If precise sector input is unavailable, construct against explicit angle references and label approximation. The reference circle is an ordinary object requiring an intentional export visibility choice.

## Calculate 144 degrees from circumference ratio

Base circumference is120 pi and the full radius150 circle circumference300 pi. The required arc is two fifths of the full circle, so its central angle is360 times two fifths =144 degrees. Preserve these three steps externally before entering labels; approximating pi as three is not an exact arc calculation. Since144 is less than180, the sector occupies less than a semicircle. A larger-than-semicircle shape fails even with the correct printed angle. Label and outline must encode the same proportion.

## Name the arc and both seam edges distinctly

Label the sector arc as corresponding to base circumference, both radial edges with the same seam identifier and the centre as apex. The arc is not slant height, and the two radial lengths totalling300 are not base circumference. Draw the radius60 base circle separately, identifying a separate surface rather than a hole at the sector centre. Place it beside the sector with a correspondence leader instead of claiming a cutting-ready arrangement. Inspect boundary labels without fill before colouring, distinguishing arc, radial edges and base circle.

## Keep allowance outside ideal arc calculations

For allowance illustration, duplicate the view and add a pale strip outside one radial edge, labelled additional allowance without changing144 degrees. Real bonding, cutting and materials are outside scope; the strip has no production specification. Retain the original radial boundary rather than incorporating allowance and claiming the complete outer outline exactly represents the lateral surface. Preserve the allowance-free view and limit arc checks to the ideal surface. Extra colour blocks do not compensate thickness, overlap or assembly errors and are not physical closure tests.

## Halve the angle when base radius halves

Duplicate with base radius30 and slant height still150. Circumference60 pi is one fifth of the full reference circle, giving72 degrees. Sector radius stays unchanged rather than halving the whole group. Base diameter changes120 to60; an optional displayed vertical height must also update to approximately146.969. List changed and retained quantities instead of changing one radius label while retaining all others. These depict different cones, not an automatically shrinking physical paper shell.

## Check angle and approximation marks after export

Save the source and open PNG/PDF output. Inspect sector-size differences for144 versus72 degrees, equal slant radii and different base diameters. Retain approximation/diagram labels rather than deleting precision limits because of missing glyphs. A print proof checks size and common scaling, not physical rolling inferred from a screen. Hide unwanted manual angle references actively. For thickened radial lines inspect stroke/scaling rather than changing angles to repair display.

## Troubleshoot radius, arc and angle in sequence

For a small sector check mistaken use of base radius, for angle disagreement check the circumference ratio, and for equal slant/vertical heights revisit the right triangle. A halved sector radius after halving the base suggests whole-group scaling. Recompute dependent values after each change;144 is not universal. Preserve both dimension sets, calculations and output, distinguishing ideal surface from allowance. This verifies these mathematical/graphical relationships, not arbitrary automatic net checking or fabrication dimensions.

## Related tutorials and sources

[VectorPaint cylinder-side unfolding: distinguish circumference, diameter and seam allowance](<https://allluckly.cn/en/guides/vectorpaint-cylinder-side-unfolding/>), [VectorPaint canvas sizes: distinguish px, pt, mm and exported pixels](<https://allluckly.cn/en/guides/vectorpaint-canvas-units/>).

Checked on November 9, 2026: VectorPaint public version 1.0.8, requiring iOS / iPadOS 17.0 or later. Capability scope follows the [official App Store listing](<https://apps.apple.com/cn/app/id1587272880>) and [Apple public version lookup](<https://itunes.apple.com/lookup?id=1587272880&country=cn>). This is an original exercise to perform independently; use controls in your installed version. Manual construction and external records do not imply new automatic analysis features. No step-by-step physical-device, private-file or all-output-environment testing is claimed.