AmbifulWorksheets
Practice that never repeats
CBSE · Class 6 · Mathematics

Playing with Constructions

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
What is the diameter of a circle of radius 5 cm?
  1. 2.5 cm
  2. 10 cm
  3. 25 cm
  4. 7 cm
2.
A circle has a diameter of 32 cm. How wide must the compass be opened to draw it?
  1. 16 cm
  2. 32 cm
  3. 64 cm
  4. 17 cm
3.
The instrument used to draw a circle is a:
  1. protractor
  2. ruler
  3. compass
  4. set square
4.
A circle has a radius of 12 cm. A point is 3 cm from its centre. The point lies:
  1. outside the circle
  2. at the centre
  3. on the circle
  4. inside the circle
5.
What is the perimeter of a rectangle 18 cm long and 2 cm wide?
  1. 40 cm
  2. 20 cm
  3. 36 cm
  4. 38 cm
6.
The diagonals of a rectangle are each 18 cm long. How far is it from the corner to the point where they cross?
  1. 9 cm
  2. 36 cm
  3. 18 cm
  4. 10 cm
7.
To draw a circle of radius 4 cm, the compass is opened to:
  1. 16 cm
  2. 4 cm
  3. 8 cm
  4. 2 cm
8.
Two circles have radii 7 cm and 3 cm, and their centres are 9 cm apart. The circles:
  1. cross at two points
  2. are the same circle
  3. touch at one point
  4. do not meet
Section B — Short answer8 × 2 = 16 marks
9.
A rectangle has a perimeter of 38 cm and a length of 14 cm. Find its width.
10.
A square has a perimeter of 16 cm. How long is each side? What is each angle?
11.
5 circles, each of radius 7 cm, are drawn in a row, each touching the next, with their centres on one line. How long is the row from end to end?
12.
A circle has a radius of 10 cm. Points P, Q and R are 14 cm, 3 cm, 13 cm from its centre. Say whether each is inside, on or outside the circle.
13.
Two circles of radii 10 cm and 9 cm touch from the outside. How far apart are their centres?
14.
A rectangle is 8 cm by 6 cm. How many right angles does it have, and what is the total length of its four sides?
15.
The diagonals of a square are 38 cm long. How long is the other diagonal, and at what angle do they cross?
16.
A chord passes through the centre of a circle of radius 22 cm. What is this chord called, and how long is it?
Section C — Word problems4 × 4 = 16 marks
17.
Vikram has a piece of wire 130 cm long and bends it into a rectangle 62 cm long, using all of the wire. How wide is the rectangle? If it were bent into a square instead, how long would each side be?
18.
A circular flower bed has a radius of 10 m. A straight path is made across it, through the centre. How long is the path? A gardener stands on the edge of the bed. How far is the gardener from the centre?
19.
Round tokens of radius 3 cm are laid in a straight line along a ruler, each touching the next. How many tokens fit exactly along 60 cm? How far apart are the centres of the first and last tokens?
20.
Vikram draws a square of side 12 cm and then a circle with its centre at one corner and radius 12 cm. How many corners of the square lie on the circle? How long is the diameter of the circle?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 6 · Mathematics

Answer key

Playing with Constructions · AW-6M-CON-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(b) 10 cm2 × 5 = 10
2(a) 16 cmthe compass opening is the radius: 32 ÷ 2 = 16
3(c) compass—
4(d) inside the circlecompare 3 cm with the radius 12 cm
5(a) 40 cm2 × (18 + 2) = 40
6(a) 9 cmthe diagonals cut each other in half: 18 ÷ 2
7(b) 4 cmthe gap is the radius
8(a) cross at two points9 is between 4 and 10
95 cm38 ÷ 2 = 19; 19 − 14 = 5
104 cm; 90°16 ÷ 4 = 4
1170 cm5 diameters: 5 × 14 = 70
12P outside, Q inside, R outsidecompare each distance with 10 cm
1319 cm10 + 9 = 19
144 right angles; 28 cm8 + 6 + 8 + 6 = 28
1538 cm; 90°the diagonals of a square are equal and cross at right angles
16a diameter; 44 cm2 × 22 = 44
173 cm wide; square side 32.5 cm130 ÷ 2 − 62 = 3; 130 ÷ 4 = 32.5
1820 m; 10 mthe path is a diameter (2 × 10); every point on the edge is one radius away
1910 tokens; 54 cmeach token takes 6 cm: 60 ÷ 6 = 10; 9 gaps of 6 cm
202 corners; 24 cmthe two corners next to the centre are 12 cm away; the far corner is farther