This MCQ module is based on: Artwork and Basic Constructions
TOPIC 29 OF 41
Artwork and Basic Constructions
🎓 Class 6
Mathematics
CBSE
Theory
Ch 8 — Playing with Constructions
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Artwork and Basic Constructions
Targeting Class 6 level in Geometry, with Basic difficulty.
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8.1 Artwork with a Compass & Ruler
Every great artist begins with two simple tools: a ruler? and a compass?. Together, they let you draw straight lines, circles, and countless beautiful patterns. In this chapter we play with these tools to make geometric art — starting from dots, lines and circles, and building up to squares, rectangles, and more.
Look at Fig 8.1 — a page of simple artwork: pairs of touching circles, concentric rings, three overlapping circles, a mouse-like face, and crossed sticks ending in small circles. Each is made using only a ruler and a compass.
Sample artwork — all drawn with ruler & compass.
Exploring the Compass
Mark a point P in your notebook. Open the compass to 4 cm. Place the tip on P and mark many points at 4 cm from P. Imagine marking all such points in every direction — what shape do you see?
A circle?! The fixed point P is the centre. The distance 4 cm is the radius. Every point on the circle is exactly 4 cm from P.
Fig 8.2 — Circle with centre P and radius 4 cm.
Definition
All points of a circle lie at the same distance from its centre. This fixed distance is the radius. Using this property, we can construct many figures precisely with a compass.
Construct: A Person (Square + Semicircle)
Look at the figure below — a "person" made of a square with a round head and a little neck. Two components:
(a) a square as the body; (b) a circle above it as the head. A curve connects them.
The challenge: the dashed curve joins the top two corners of the square passing near the head. Use a compass to find the right centre and radius.
Construct: A Wavy Wave
The wavy wave is made of two half-circles: one above the central line, one below. If \(AB = 8\) cm is the central line, the first wave is drawn as a half-circle of diameter \(AX=4\) cm above line AB.
Wavy wave: two half-circles of equal diameter on opposite sides of AB.
Try This: What radius should be taken in the compass to get this half-circle? What should be the length of AX?
Answer: Radius = 2 cm (half of AX). AX itself should be 4 cm.
Answer: Radius = 2 cm (half of AX). AX itself should be 4 cm.
Figure it Out (p.193)
Q1. What radius should be taken in the compass to get the half-circle of the wavy wave? What should be the length of AX?
Radius = 2 cm. AX = 4 cm (half of AB).
Q2. Take a central line of a different length and try to draw the wave on it.
Example: Let AB = 10 cm. Find midpoint X at 5 cm. Radius = 2.5 cm. Draw upper half-circle from A to X, lower half-circle from X to B.
Q3. Try to recreate the figure where the waves are smaller than a half circle (as in "A Person"). The challenge here is to get both the waves to be identical.
Use the same radius for both arcs but place the compass tip further away from AB so only a part of each circle appears above and below the line. Both arcs will be congruent.
Activity: First Circle Hunt
L3 ApplyMaterials: Compass, ruler, pencil, blank notebook.
Predict: If you mark many points that are 3 cm from a fixed point P, what shape will all those points form?
- Mark point P in the middle of the page.
- Open the compass to 3 cm using the ruler.
- Place the tip at P and, holding it still, rotate the pencil end to trace.
- Examine: is the curve a circle? Measure a few points; are they all 3 cm from P?
Yes — every point on the curve is exactly 3 cm from P. This is the defining property of a circle: all points equidistant from the centre.
Competency-Based Questions
Scenario: A crafts teacher gives students a task: use a compass to draw three overlapping circles such that each pair of circles has the distance between their centres equal to the common radius (5 cm).
Q1. If the radius is 5 cm, what is the distance between the centres of any two adjacent circles?
L3 Apply5 cm — same as the radius.
Q2. Where do any two of these circles cross each other? Analyse.
L4 AnalyseAt two points which are each 5 cm from both centres. These two intersection points lie on the perpendicular bisector of the line joining the centres.
Q3. A student claims: "If I use a 4 cm radius but centres 6 cm apart, the two circles will still intersect." Evaluate.
L5 EvaluateTrue — they intersect as long as the distance between centres is less than twice the radius (here 8 cm) and more than 0. 6 cm < 8 cm, so they intersect at two points.
Q4. Design a "flower" pattern using one central circle of radius 4 cm and 6 outer circles of the same radius, whose centres lie on the central circle. Describe your construction steps.
L6 Create1. Draw central circle of radius 4 cm with centre O. 2. Mark any point on the circle as first centre. 3. Without changing compass radius, step around the circle making 6 arc intersections — these will be the 6 centres. 4. Draw circles of radius 4 cm at each of the six centres. Result: classic "flower of life" pattern with 6-fold symmetry.
Assertion–Reason Questions
A: Every point of a circle is equidistant from its centre.
R: This equal distance is called the radius.
R: This equal distance is called the radius.
(b) — Both statements are true, but R defines the term "radius" rather than explaining the property stated in A.
A: A compass draws circles of arbitrary size.
R: The compass angle can be fixed to any chosen radius using a ruler.
R: The compass angle can be fixed to any chosen radius using a ruler.
(a) — Both true, and R correctly explains why (a).
A: The wavy wave on AB has two half-circles, one above and one below AB.
R: The two half-circles have different radii.
R: The two half-circles have different radii.
(c) — A is true. R is false — both half-circles have the same radius so the wave is symmetric.
Frequently Asked Questions
What tools are used in Class 6 geometric constructions?
A sharpened pencil, a ruler for straight lines and measuring, and a compass for drawing circles and arcs of any required radius.
How do you draw a circle of radius 4 cm?
Set the compass opening to 4 cm against the ruler, fix the pointer at the centre on the paper, and rotate the pencil end in one smooth motion to complete the circle.
Why is accuracy important in constructions?
Accurate constructions give correct angles, equal sides and reliable measurements. Small errors in compass or ruler use compound into large mistakes in geometric figures.
What artwork can be made with just lines and circles?
Many patterns such as flower rosettes, overlapping arcs, square tiles and mandalas are made with just straight lines and circles arranged by construction.
Can you construct a figure without a ruler?
Some figures can be constructed using only a compass, but most Class 6 constructions use both a ruler and a compass for accuracy and convenience.
AI Tutor
Mathematics Class 6 — Ganita Prakash
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