Chapter 8 · Model TestAttempt first – solutions on the next page

Model Test Paper മാതൃകാ ചോദ്യപേപ്പർ

Set a timer for 1½ hours, keep the textbook closed, and write your answers in a notebook. Show your working and give units. Then check your work on the solved paper, which also shows how marks are given.

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Kerala State Syllabus · Standard IX · Mathematics Part 2

MATHEMATICS – Chapter 8: Measures of Circles (വൃത്തങ്ങളുടെ അളവുകൾ)

Time: 1½ hoursMaximum marks: 40
Instructions: Answer all questions. Answers may be left in terms of π unless a question asks for a decimal value; use π ≈ 3.14 or 3.1416 where a decimal is asked. Give units. Marks are given for correct steps even when the final answer is wrong. Section A: 8 × 1 = 8, Section B: 5 × 2 = 10, Section C: 4 × 3 = 12, Section D: 2 × 5 = 10.
SECTION A – Answer all questions8 × 1 = 8 marks
1.
The circumference of a circle of radius 7 cm is (in terms of π).
(1)
2.
The area of a circle of radius 3 cm is (in terms of π).
(1)
3.
If the diameter of a circle is doubled, its circumference becomes
(a) the same(b) twice(c) four times(d) half
(1)
4.
A circle has circumference 10π cm. Its diameter is .
(1)
5.
A circle has area 49π sq cm. Its radius is .
(1)
6.
π correct to four decimal places is .
(1)
7.
Area of a circle = ½ × × radius.
(1)
8.
The Kerala mathematician who found a series for π is
(a) Aryabhata(b) Madhavan(c) Brahmagupta(d) Bhaskara
(1)
SECTION B – Answer all questions5 × 2 = 10 marks
9.
A wire 31.4 cm long is bent into a circle. Find its diameter (take π ≈ 3.14).
(2)
10.
A chord of length 8 cm is 3 cm from the centre of a circle. Find the circumference and the area of the circle.
(2)
11.
Find the area of the ring between two circles with the same centre and radii 5 cm and 3 cm.
(2)
12.
A square has side 4 cm. Find the area of the circle drawn inside it touching all four sides, and of the circle passing through its four corners.
(2)
13.
Two circles have radii 3 cm and 6 cm. Find the ratio of their circumferences and the ratio of their areas.
(2)
SECTION C – Answer all questions4 × 3 = 12 marks
14.
A regular hexagon of side 3 cm is drawn inside a circle with its corners on the circle. Find the difference between the areas of the circle and the hexagon, correct to two decimal places.
(3)
15.
An isosceles triangle with base 6 cm and height 9 cm has its three corners on a circle. Find the circumference of the circle.
(3)
16.
A rectangle 6 cm × 8 cm has its corners on a circle. Find the area of the circle and the area of the part of the circle outside the rectangle (to two decimal places).
(3)
17.
Three circles of diameters 2 cm, 4 cm and 6 cm have their centres on a diameter of a circle of diameter 12 cm and together fill that diameter. Show that the sum of their circumferences equals the circumference of the big circle.
(3)
SECTION D – Answer all questions2 × 5 = 10 marks
18.
  1. Using regular polygons drawn inside a circle, explain why the area of a circle is ½ × circumference × radius.
  2. Hence show that the area is πr².
  3. Show that the ring between circles of radii 5 cm and 4 cm (same centre) has the same area as a circle of radius 3 cm.
  4. Explain why this happens.
(5)
19.
A regular hexagon has sides 4 cm. Arcs of radius 2 cm are drawn inside it with each corner as centre, and the parts cut off are removed.
  1. Find the area of the hexagon.
  2. Find the total area of the six parts cut off.
  3. Find the area of the star-shaped part left.
  4. Find the total length of the six arcs.
(5)
✔ Finished?

Mark your answers using the solved paper. For each mistake, the solution tells you which page of this guide to revisit.