Grade 10 — Mathematics 10-3 › T3U03 Linear Measurement Problems

Grade 10 › T3U03 Linear Measurement Problems › L2
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-M3

L2 · Measuring well: inside and outside diameters, midpoints

Learning goal

“I can measure and calculate inside and outside diameters of pipes and tubes with a caliper, and I can find the midpoint of any length - decimals or fractions - and explain the strategy I used.”

Outside diameter (OD) — the distance across the OUTSIDE of a pipe or tube, through its centre. A caliper's jaws closing around a pipe read the OD.
Inside diameter (ID) — the distance across the open INSIDE of a pipe - the space a fitting or another pipe must fit into.
Wall thickness — the thickness of the pipe's material. A pipe has TWO walls across any diameter line: ID = OD - 2 x wall thickness.
Midpoint — the point exactly halfway along a length. Finding it is halving: midpoint measurement = length / 2.
Worked example

A caliper closes around the outside of a pipe and reads 8.4 cm. The pipe wall is 0.3 cm thick. Find the inside diameter. Step 1: Draw the diameter line in your head: wall - open space - wall. The line crosses the wall material TWICE. Step 2: ID = OD - 2 x wall = 8.4 - 2 x 0.3 = 8.4 - 0.6. Step 3: ID = 7.8 cm. Verify: 7.8 + 0.6 = 8.4 - the ID rebuilds the OD.

Check yourself — explain it

Why is the wall thickness subtracted TWICE?

Paired problem — example still visible

A pipe has OD 5.0 cm and wall thickness 0.2 cm. Find the ID. -> 4.6 cm (5.0 - 2 x 0.2 = 5.0 - 0.4)

Faded completion — last step is yours

"A copper tube has OD 2.2 cm and wall 0.15 cm. ID = 2.2 - 2 x ___ = 2.2 - 0.30 = ___ cm." -> 0.15; 1.90 cm

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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