Unit 3: Mensuration, Calendar, and Clocks - Practice Quiz

1 What is the total surface area of a cube with side length ?

2 What is the volume of a cube whose side length is cm?

3 Which formula gives the volume of a cuboid with length , breadth , and height ?

4 Find the total surface area of a cuboid with length cm, breadth cm, and height cm.

5 What is the surface area of a sphere with radius cm?

6 Which formula gives the volume of a sphere of radius ?

7 What is the total surface area of a hemisphere of radius , including its circular base?

8 What is the volume of a hemisphere with radius cm?

9 Which formula gives the curved surface area of a cone with radius and slant height ?

10 Find the volume of a cone with radius cm and height cm.

11 What is the curved surface area of a cylinder with radius and height ?

12 Find the volume of a cylinder with radius cm and height cm.

13 How many days are there in an ordinary year?

14 Which of the following years is a leap year?

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

16 How many days does February have in a leap year?

17 If January 1 is a Sunday, what day is January 8 of the same year?

18 How many complete rotations does the minute hand make in hours?

19 Through how many degrees does the hour hand move in one hour?

20 What is the smaller angle between the hour hand and the minute hand at ?

21 The volume of a cube is . What is its total surface area?

22 Eight identical solid cubes, each having an edge of , are melted to form one larger cube. What is the total surface area of the larger cube?

23 A closed cuboidal box measures . If covering material costs per , what is the total cost of covering the box?

24 A cuboidal tank has a base measuring . A solid object of volume is completely submerged in it. By how much does the water level rise?

25 The volume of a sphere is . What is its surface area?

26 If the radius of a sphere is increased by , by what percentage does its surface area increase?

27 A solid hemisphere has a radius of . Which pair gives its total surface area and volume, respectively?

28 A cone has radius and height . Using , what is its total surface area?

29 A closed cylindrical container has radius and height . Using , what is its total surface area?

30 Water from a cylindrical vessel of radius and height is poured into another cylinder of radius . What height will the water reach in the second cylinder?

31 How many odd days are there in a period of ordinary consecutive years containing exactly leap years?

32 Which of the following years is a leap year under the Gregorian calendar rules?

33 If January 1, 2024 was a Monday, what day of the week was March 15, 2024?

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

35 January 26, 2023 was a Thursday. On which day of the week did January 26, 2024 fall?

36 What is the smaller angle between the hour hand and the minute hand at ?

37 At what time between and o'clock do the two hands of a clock coincide?

38 What is the first time after when the hands of a clock are at right angles?

39 A clock gains minutes every hour. It is set correctly at a.m. When it shows p.m. on the same day, what is the correct time?

40 A clock takes seconds to strike times. How many seconds will it take to strike times at the same rate?

41 A solid cube of side cm is melted and recast into identical solid spheres of radius cm. Using and assuming no loss of material, how many spheres are formed?

42 Every face of a cube of side is painted, and the cube is divided into congruent smaller cubes. All smaller cubes having exactly two painted faces are removed. What is the volume of the remaining solid?

43 The edge lengths of a cuboid are in arithmetic progression. Its total surface area is cm, and its space diagonal is cm. What is its volume?

44 The length, breadth, and height of a cuboid are in the ratio . If its total surface area is cm, what is its volume?

45 A sphere of radius cm is cut by a plane whose perpendicular distance from the center is cm. What is the total surface area of the smaller piece, including its newly exposed circular face?

46 A hollow spherical shell with external radius cm and internal radius cm is melted into identical solid cones, each having base radius cm and height cm. How many complete cones are formed?

47 A conical cavity is carved from a solid hemisphere of radius cm. The cone has the same circular base as the hemisphere and its vertex is at the lowest point of the hemisphere. What is the total exposed surface area of the remaining solid?

48 A hemispherical bowl has external radius cm and internal radius cm. Including the inner surface, outer surface, and flat annular rim, what is its total surface area?

49 A sector of radius cm and central angle is rolled to form a cone by joining its radial edges. What is the volume of the cone?

50 A cone has height cm and base radius cm. It is cut by a plane parallel to its base at half its height measured from the vertex. What is the volume of the resulting lower frustum?

51 A hollow cylindrical pipe has external radius cm, internal radius cm, and length cm. What is its total surface area, including both annular ends?

52 A solid cylinder of radius cm and height cm is melted into identical solid spheres. By how much does the total surface area increase after recasting?

53 In the Gregorian calendar, January 1, 2001 was a Monday. What day of the week was December 31, 2400?

54 Which is the earliest year after whose calendar is identical to that of , with the same dates falling on the same weekdays?

55 If August 15, 1947 was a Friday, what day of the week was January 26, 1950?

56 Under the proleptic Gregorian calendar, March 1, 2000 was a Wednesday. What day of the week was March 1, 2100?

57 How many times are the hour and minute hands exactly perpendicular between noon and midnight, excluding both endpoints?

58 At what time between and o'clock are the hands of a clock first in a straight line but pointing in opposite directions?

59 A clock is correct at AM but gains minutes for every hours of true time. What is the true time when the clock first indicates PM that day?

60 At which two times between and o'clock is the smaller angle between the clock hands exactly ?