Unit 3: Mensuration, Calendar and Clocks - Practice Quiz

1 What is the perimeter of a square with side ?

2 What is the area of a rectangle with length and breadth ?

3 What is the volume of a cube with side ?

4 How many faces does a cuboid have?

5 What is the volume of a sphere of radius ?

6 A hemisphere is what fraction of a sphere by volume?

7 What is the volume of a cylinder with radius and height ?

8 What is the volume of a cone with radius and height ?

9 How many days are there in a week?

10 How many months are there in one year?

11 How many days are there in the month of April?

12 If today is Monday, what day will it be after 3 days?

13 If January 1 is a Monday, what day is January 8 of the same year?

14 If the 5th day of a month is Wednesday, what day is the 12th day of the same month?

15 How many odd days are there in a normal year of 365 days?

16 How many odd days are there in a leap year of 366 days?

17 How many numbers are marked on the face of a standard clock?

18 A clock gains 5 minutes every hour. How many minutes will it gain in 2 hours?

19 A clock loses 2 minutes every hour. How many minutes will it lose in 4 hours?

20 What is the angle between the hour hand and the minute hand at 3:00?

21 The length and breadth of a rectangle are in the ratio . If its perimeter is cm, what is its area?

22 A uniform path m wide is built outside a rectangular garden measuring m by m. What is the area of the path?

23 A solid cube of side cm is cut into smaller cubes, each of side cm. How many smaller cubes are formed?

24 A cuboid has length cm, breadth cm, and volume . What is its total surface area?

25 If the radius of a sphere is increased by , by what percentage does its volume increase?

26 The total surface area of a solid hemisphere is . Using , what is its volume?

27 A cone has radius cm and vertical height cm. Using , what is its curved surface area?

28 A solid cylinder of radius cm and height cm is melted to form spheres of radius cm. How many complete spheres are formed?

29 A solid consists of a cylinder of radius cm and height cm topped by a cone of the same radius and height cm. What is the total volume?

30 If January 1 of a leap year is a Monday, on which day will March 1 of that year fall?

31 An ordinary year begins on a Wednesday. On which day will the following year begin?

32 If April 10 falls on a Monday, on which day of the week will April 25 fall?

33 If the 18th day of a month is a Friday, what day of the week was the 3rd day of the same month?

34 January 1, 2025, was a Wednesday. On which day of the week was October 2, 2025?

35 What day of the week will it be days after a Saturday?

36 The calendar for the year 2021 can be reused for which of the following years?

37 How many leap years were there from 1901 through 2000, including both years?

38 At what time between 2 o'clock and 3 o'clock will the hour and minute hands coincide?

39 A clock gains minutes every real hour. It is set correctly at noon. When the clock shows 6:30 p.m., what is the correct time?

40 What is the smaller angle between the hour hand and the minute hand at 3:40?

41 The diagonals of a rhombus are in the ratio . If the radius of its inscribed circle is units, what is the area of the rhombus?

42 A trapezium has parallel sides of lengths cm and cm, while its nonparallel sides are cm and cm. What is its area?

43 A cuboid has space diagonal cm, total surface area , and volume . What is the total length of all its edges?

44 An open box is formed by cutting equal squares from the corners of a cm by cm rectangular sheet and folding up the sides. What side length of each square maximizes the volume?

45 A solid hemisphere of radius is melted and recast into a cylinder whose radius is . If no material is lost, what is the height of the cylinder?

46 One sphere circumscribes a cube, while another sphere is inscribed in the same cube. What is the ratio of the volume of the larger sphere to that of the smaller sphere?

47 A cone has base radius cm and height cm. A smaller cone with base radius cm is removed by a cut parallel to the base. What is the total surface area of the remaining frustum, including both circular ends?

48 A closed right circular cylinder has fixed volume . What is its minimum possible total surface area?

49 How many odd days are contributed by the calendar years from through , inclusive, under Gregorian calendar rules?

50 How many days elapsed from August 15, 1947, to January 26, 1950, excluding the starting date but including the ending date?

51 January 1, 2000 was a Saturday. What day of the week was May 17, 2040?

52 Using the proleptic Gregorian calendar, January 1, 2000 was a Saturday. What day of the week was July 4, 1776?

53 What is the first year after whose calendar is identical to that of ?

54 In a leap year, January 1 falls on a Wednesday. On which weekday does December 31 fall, and how many months begin on a Sunday?

55 Between 2:00 and 3:00, the hour and minute hands are at equal angular distances from the 12-mark at two distinct instants. What is the later instant?

56 A clock is set correctly at noon on Monday and gains minutes every actual hours. What is the actual time when the clock first displays 1:00 p.m. on Thursday?

57 Two clocks are set correctly at noon. Clock A gains minutes per day, while clock B loses minutes per day. When their displayed times first differ by exactly one hour, what do they display?

58 At what first instant after 7:00 do the hands of a clock form a right angle?

59 At what time between 4:00 and 5:00 is the minute hand exactly ahead of the hour hand?

60 Between 3:00 and 4:00, the hands of a clock form an angle of at two instants. What is the sum of the numbers of minutes after 3:00 at those instants?