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Estimation (guesstimates) · 5 marks

Solve the following:

  1. (i) Could a person drink enough water in a lifetime to fill an entire room the size of your classroom?
  2. (ii) Estimate the number of bricks used to build the walls of your classroom.
Answer: (i) No. A classroom about 8 m × 6 m × 3.5 m holds 168 m3 = 1,68,000 L; a person drinking about 2.5 L a day for 75 years drinks about 68,000 L, only about 40% of the room. (ii) Walls of about 18.5 m3 of brickwork, with each brick (with mortar) about 20 cm × 10 cm × 10 cm = 0.002 m3: about 9000 bricks.

Step-by-step solution

Idea: Model each quantity with simple shapes and sensible everyday numbers, state the assumptions, then compare or divide.

(i) Could a person drink enough water in a lifetime to fill an entire room the size of your classroom?

  1. Guess: perhaps yes? Assume the classroom is 8 m × 6 m × 3.5 m: volume = 168 m3 = 168 × 1000 = 1,68,000 L.1 mark
  2. A person drinks about 2.5 L a day for about 75 years: 2.5 × 365 × 75 ≈ 68,400 L.1 mark
  3. 68,400 < 1,68,000, so no: a lifetime of drinking fills only about 40% of the room.½ mark
No: about 68,000 L in a lifetime against about 1,68,000 L for the room (about 40%).

(ii) Estimate the number of bricks used to build the walls of your classroom.

  1. Walls: perimeter 2(8 + 6) = 28 m, height 3.5 m, thickness 0.2 m: 28 × 3.5 × 0.2 = 19.6 m3.1 mark
  2. Subtract a door (1 m × 2.1 m) and two windows (1.5 m × 1.2 m each): 5.7 m2 × 0.2 m = 1.14 m3. Brickwork ≈ 19.6 − 1.14 ≈ 18.5 m3.½ mark
  3. One brick with its mortar ≈ 20 cm × 10 cm × 10 cm = 0.002 m3. Number ≈ 18.5 ÷ 0.002 ≈ 9250, so about 9000 bricks.1 mark
About 9000 bricks.
(i) No: about 68,000 L drunk in a lifetime vs about 1,68,000 L to fill an 8 m × 6 m × 3.5 m classroom. (ii) About 9000 bricks.

Check: (i) 1 m3 = 1000 L, so 168 m3 = 1,68,000 L ✓. (ii) Builders use about 500 bricks per m3 of brickwork: 18.5 × 500 ≈ 9250 ✓.

Answer to write in the exam

(i)

Classroom = 8 × 6 × 3.5 = 168 m3 = 1,68,000 L

Lifetime drinking ≈ 2.5 × 365 × 75 ≈ 68,400 L

68,400 < 1,68,000

∴ No, only about 40% of the room

(ii)

Wall volume = 28 × 3.5 × 0.2 = 19.6 m3

Openings = 5.7 × 0.2 = 1.14 m3 ⇒ brickwork ≈ 18.5 m3

One brick (with mortar) = 0.2 × 0.1 × 0.1 = 0.002 m3

∴ Number ≈ 18.5 ÷ 0.002 ≈ 9000 bricks

Common mistakes that cost marks

  • Forgetting that 1 m3 = 1000 litres.
  • Counting the floor and ceiling as brick walls.
  • Using the brick size without mortar and without subtracting doors and windows (small effect, but should be stated).

How this can come in the exam

Case-based (4 marks)

A boundary wall is 20 m long, 2 m high and 0.25 m thick. Bricks with mortar measure 25 cm × 12.5 cm × 8 cm.
(i) Find the volume of the wall. (ii) Find the volume of one brick in m3. (iii) How many bricks are needed? (iv) If 110 of the wall is mortar instead, how many bricks are needed?

Show answer(i) 20 × 2 × 0.25 = 10 m3 (1 mark). (ii) 0.25 × 0.125 × 0.08 = 0.0025 m3 (1 mark). (iii) 10 ÷ 0.0025 = 4000 (1 mark). (iv) 9 ÷ 0.0025 = 3600 (1 mark).

Try one yourself

Estimate how many 1-litre bottles of water would fill a room 4 m × 3 m × 3 m.

Show answer

36 m3 = 36,000 L, so 36,000 bottles.

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