GeographyCBSE Class 11 · Map Projections

Conical Projection with One Standard Parallel and Mercator's Projection (Class 11 Practical Work in Geography, Chapter 4)

Updated 17 October 2026 · Fact-checked

The conical projection with one standard parallel projects the graticule on a cone touching one parallel: parallels are concentric arcs, meridians straight lines meeting at the pole, scale true along the standard parallel and all meridians. Mercator's projection (1569) is orthomorphic with parallel straight lines at right angles; straight lines are rhumb lines, ideal for navigation, but polar areas are greatly exaggerated.

Conical: arcs and straight meridians, true scale on the standard parallel. Mercator: right-angle grid, straight rhumb lines, but polar areas grow huge.

Illustration drawn for QuestionBuddy.

Understand Conical Projection with One Standard Parallel and Mercator's Projection: Properties, Construction and Uses

Why this topic matters. CBSE limits the practical to these two projections; properties, uses and limits are asked in the written test and the construction values are asked in numerical form.

1. Conical principle. The graticule is projected on a cone that touches the globe along one parallel, the standard parallel, usually the middle parallel of the area. NCERT's example: area 10 to 70 degrees N, 10 to 130 degrees E, scale 1:250,000,000, interval 10 degrees. Reduced earth radius R = 640,000,000 / 250,000,000 = 2.56 cm. Standard parallel 40 degrees N and central meridian 70 degrees E (the middle values).

2. Construction values. Spacing between parallels = 2 x pi x R x interval / 360 = about 0.447 cm. Radius of the standard parallel on the cone = R cot (40 degrees) = about 3.05 cm. Spacing of meridians along the standard parallel = 2 x pi x R cos 40 x interval / 360 = about 0.342 cm. Steps: draw the central meridian, draw the standard parallel as an arc of radius 3.05 cm, mark other parallels at 0.447 cm along the central meridian as concentric arcs, mark meridians along the standard parallel at the meridian spacing, and join them to the pole with straight lines.

3. Properties of the conical projection. (i) Parallels are arcs of concentric circles, equally spaced. (ii) Meridians are straight lines meeting at the pole, cutting parallels at right angles. (iii) Scale is true along all meridians. (iv) The pole is an arc of a circle. (v) Scale is true along the standard parallel and exaggerated away from it. (vi) Meridians become closer towards the pole. (vii) It is neither equal area nor orthomorphic.

4. Limits and uses of the conical projection. Unsuitable for a world map or large areas. Suitable for mid-latitude areas with small latitudinal and larger longitudinal extent, and for long narrow east-west strips: railways, roads, narrow river valleys and international boundaries, for example the Canadian Pacific Railway, the Trans-Siberian Railway, the USA-Canada boundary and the Narmada valley.

5. Mercator's projection. Developed by the Dutch cartographer Gerardus Mercator in 1569, based on mathematical formulae, and orthomorphic. Parallels and meridians are straight lines at right angles to each other, and the spacing between parallels increases towards the poles. A straight line on the map is a rhumb line (loxodrome), a line of constant bearing, so the projection is ideal for navigation. Areas are greatly exaggerated towards the poles (Greenland appears as large as the USA), so it is unsuitable for showing area distribution.

Conical Projection with One Standard Parallel and Mercator's Projection: Properties, Construction and Uses: key facts

Conical values (NCERT example): $R = 640, 000, 000/250, 000, 000 = 2.56 c m ∣ S t an d a r d p a r a l l e l 40 d e g r ees N ∣ P a r a l l e l s p a c in g ab o u t 0.447 c m ∣ S t an d a r d p a r a l l e l r a d i u s ab o u t 3.05 c m ∣ M er i d ian s p a c in g ab o u t 0.342 c m$; Interval 10 degrees.
Conical properties: Parallels: concentric arcs
Meridians: straight lines to the pole
True scale along standard parallel and all meridians; Neither equal area nor orthomorphic.
Mercator: Year 1569
Orthomorphic
Straight parallels and meridians at right angles
Parallel spacing increases poleward
Rhumb lines straight; Navigation.
Uses: Conical: mid-latitude east-west strips, railways, boundaries | Mercator: navigation charts, equatorial region maps; Not for world area comparison.

How to answer Conical Projection with One Standard Parallel and Mercator's Projection: Properties, Construction and Uses questions

Construction values come from three formulas.

1Compute R as earth radius divided by the scale denominator.
2Find parallel spacing = 2 pi R x interval / 360.
3Find the standard parallel radius = R cot of its latitude.
4Find the meridian spacing = 2 pi R cos latitude x interval / 360.

Conical Projection with One Standard Parallel and Mercator's Projection: Properties, Construction and Uses in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Railway line on a map

Suppose a planner wants a map of a long, narrow east-west railway running along 45 degrees N in a mid-latitude country.

Which projection suits it, and why?

Try it first, then show the solutionSolution

A long east-west strip along the standard parallel is shown correctly.
Scale is true along the standard parallel.

Answer: Conical projection with one standard parallel.

Memory hook: Strip along the parallel.

Sailing straight

Suppose a ship wants to hold one compass bearing across the ocean and draws a straight line on the chart.

Which projection and which line is this?

Try it first, then show the solutionSolution

Mercator's projection.
The line is a rhumb line of constant bearing.

Answer: Mercator's projection; the straight line is a rhumb line (loxodrome).

Memory hook: Straight line equals constant bearing.

Tricks to remember Conical Projection with One Standard Parallel and Mercator's Projection: Properties, Construction and Uses

Short memory aids. Say each one aloud once, then use it on a question the same day.

Standard parallel is the middle
Choose the middle parallel of the area
Use it when: Conical.
Mercator 1569
Orthomorphic, rhumb line, poles exaggerated
Use it when: Mercator.
Greenland and USA
Greenland looks as big as the USA
Use it when: Distortion example.

Conical Projection with One Standard Parallel and Mercator's Projection: Properties, Construction and Uses: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Mercator year · 1 mark · MCQBoard level

Mercator's projection was developed in:
(A) 1469
(B) 1569
(C) 1669
(D) 1769

Try it first, then show the solutionSolution

Gerardus Mercator in 1569 (1 mark).

Answer: (B)

Example 2: Standard parallel · 2 marks · Very short answerBoard level

What is a standard parallel and where is the scale true in the conical projection? (2 marks)

Try it first, then show the solutionSolution

The parallel along which the cone touches the globe (1 mark).
Scale is true along it and along all meridians (1 mark).

Answer: The standard parallel is the parallel along which the cone touches the globe, usually the middle parallel of the area. In the conical projection scale is true along it and along all meridians.

Example 3: R and spacing · 3 marks · Short answerHarder board level

Using R = 2.56 cm for a conical projection with a 10 degree interval, show that parallels are about 0.447 cm apart. (3 marks)

Try it first, then show the solutionSolution

Spacing = 2 x pi x R x interval / 360 (1 mark).
= 2 x 3.1416 x 2.56 x 10 / 360 (1 mark).
= 16.085 x 10 / 360 = 0.447 cm (1 mark).

Answer: Parallel spacing = 2 x pi x R x 10 / 360 = 2 x 3.1416 x 2.56 x 10 / 360 = 160.85 / 360 = about 0.447 cm.

Example 4: Assertion and reason: Mercator · 1 mark · Assertion-reasonHarder board level

Assertion (A): Mercator's projection is ideal for navigation.
Reason (R): A straight line on it is a rhumb line of constant bearing.
(A) Both true, R explains A
(B) Both true, R does not explain A
(C) A true, R false
(D) A false, R true

Try it first, then show the solutionSolution

Constant bearing along a straight line explains the navigational value (1 mark).

Answer: (A)

Example 5: HOTS: standard parallel radius · 5 marks · Long answerHOTS / competency

For the conical projection of NCERT's example (R = 2.56 cm, standard parallel 40 degrees N, interval 10 degrees), compute the radius of the standard parallel arc and the spacing of meridians along it, and explain why the conical projection is poor for a world map. (5 marks)

Try it first, then show the solutionSolution

Radius = R cot 40 degrees = 2.56 x 1.1918 (1 mark).
= about 3.05 cm (1 mark).
Meridian spacing = 2 x pi x 2.56 x cos 40 x 10 / 360 = 0.447 x 0.766 (1 mark).
= about 0.342 cm (1 mark).
A world map would be extremely distorted, especially in the hemisphere opposite the standard parallel (1 mark).

Answer: The radius of the standard parallel is R cot 40 = 2.56 x 1.1918 = about 3.05 cm. The meridian spacing along it is 2 x pi x 2.56 x cos 40 x 10 / 360 = 0.447 x 0.766 = about 0.342 cm. The conical projection is unsuitable for a world map because distortion becomes extreme away from the standard parallel, especially in the opposite hemisphere, and even within one hemisphere it suits only mid-latitude areas with limited latitudinal extent.

Where students lose marks in Conical Projection with One Standard Parallel and Mercator's Projection: Properties, Construction and Uses

The slips examiners see most often, and what to write instead.

Mistake: Saying the conical projection is equal area
Sounds well designed.
Wrong working
It preserves area.
Right working
It is neither equal area nor orthomorphic.
Do this: Learn the property list.
Usually costs: 1 mark.
Mistake: Using degrees directly without converting R
Formula slip.
Wrong working
R = 640,000,000 x 250,000,000.
Right working
R = 640,000,000 / 250,000,000 = 2.56 cm.
Do this: Divide.
Usually costs: 1 mark.
Mistake: Saying Mercator preserves area
Orthomorphic confused with equal area.
Wrong working
Mercator is equal area.
Right working
Mercator is orthomorphic; area is exaggerated near the poles.
Do this: Name Greenland example.
Usually costs: 1 mark.

Exam tips

Show R, spacing and radius formulas with substitution.
Write the properties as a numbered list.
Give one use and one limitation for each projection.

Practice questions on Conical Projection with One Standard Parallel and Mercator's Projection: Properties, Construction and Uses

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
Which projection shows rhumb lines as straight lines?
(A) conical
(B) Mercator
(C) gnomonic
(D) zenithal
Hint
Navigation.
Answer
(B)
Q2 · 2 marks · Very short answerBoard level
Give two uses of the conical projection with one standard parallel. (2 marks)
Hint
Strips.
Answer
It is used for mid-latitude east-west strips such as the Trans-Siberian Railway or the Canadian Pacific Railway, and for the USA-Canada boundary or the Narmada valley.
Q3 · 3 marks · Short answerHarder board level
State three properties of the conical projection. (3 marks)
Hint
Parallels, meridians, scale.
Answer
Parallels are arcs of concentric circles, meridians are straight lines meeting at the pole, and the scale is true along the standard parallel and all meridians but exaggerated away from the standard parallel.
Q4 · 3 marks · Short answerHarder board level
Describe the limitations of Mercator's projection. (3 marks)
Hint
Polar areas.
Answer
Areas are greatly exaggerated towards the poles; Greenland appears as large as the USA. Parallel spacing increases poleward, so the projection is unsuitable for showing the distribution of area or for polar regions, though it suits navigation.
Q5 · 4 marks · Short answerHOTS / competency
A cartographer must map the Narmada valley and a navigator must plot a ship's course. Choose the projection for each, give the property that makes it suitable and name one limitation of each. (4 marks)
Hint
Strip versus bearing.
Answer
The Narmada valley is a narrow east-west strip in mid-latitudes, suited to the conical projection with one standard parallel, whose scale is true along the standard parallel; its limitation is distortion away from it. The ship's course suits Mercator's projection, in which a straight rhumb line gives constant bearing; its limitation is the exaggeration of area towards the poles.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Who developed Mercator's projection?Show answer
Gerardus Mercator, in 1569.
2.What are meridians in the conical projection?Show answer
Straight lines meeting at the pole.
3.What is a loxodrome?Show answer
A rhumb line of constant bearing.
4.What is R for 1:250,000,000?Show answer
2.56 cm.

Conical Projection with One Standard Parallel and Mercator's Projection: Properties, Construction and Uses: frequently asked questions

Why is the standard parallel chosen at the middle?

To reduce distortion at the edges of the area.

Is Mercator suitable for polar regions?

No; polar areas are greatly exaggerated.

What is orthomorphic?

True shape, usually at the cost of area.