Page 306 - ICSE Math 8

37. Rotate points A(0, –1) and B(2, 3) clockwise through an angle of 90° and C(4, 0) and D(–3, 3) anticlockwise
through an angle of 90° about the origin. Find the coordinates of the points obtained.
38. The smallest angle through which a geometrical figure has to be rotated about a point O to coincide
with its original position is 60°. Find the order of rotational symmetry of the figure.
39. Given that PQ is a tangent to a circle with P as the point of contact. If the radius of the circle with centre
O is 6 cm and PQ = 8 cm, find the length of OP.
40. A quadrilateral ABCD is drawn to circumscribe a circle with centre O. Prove that AB + CD = AD + BC.
41. A path of uniform width 1.5 m runs outside a rectangular plot of dimension 25 m by 15 m. Find the
area of the path. Find the cost of paving the path at the rate of ` 125.50 per metre square.
42. Find the area of a triangle with sides 25 cm, 18 cm and 12 cm.
43. Find the total surface area (TSA), lateral surface area (LSA) and length of the diagonal of a cuboid of
dimensions 12 cm × 0.6 dm × 8 cm.
44. Find the area levelled by a cylindrical roller of diameter 40 cm and length 3.5 m in 120 revolutions.
45. Convert 1–20, 21–40, 41–60, etc., into exclusive class intervals.
46. Given are some inclusive class intervals: 5–15, 16–26, 27–37 and 38–48. Find the value of h and convert
into exclusive class intervals.
47. A fair die is rolled once. What is the probability of getting a number less than 5?
48. Find the probability that a leap year selected at random will have 53 Mondays.

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