L8 · Surface Area and Volume Clinic

Learning goal

“I can look at any problem in this unit and choose correctly: surface area or volume, which solid, which height (slant or vertical), which faces exist - then execute, and run any of the formulas backwards to find an unknown dimension.”

Decision first — before calculating, state: covers or fills? (units2 or units3), which solid(s), which height, open or closed. Four answers, THEN arithmetic.

Working backwards — when the surface area or volume is given, substitute the known values and divide out the known factors to free the unknown dimension (indicator 3.4); always verify by substituting back.

Worked example

"A conical tent (with a floor) has radius 4 m and slant height 7 m. How much canvas is in the tent?" Decision: canvas COVERS -> surface area. Solid: cone, CLOSED (floor). Height: slant (given). Execute: SA = π x 16 + π x 4 x 7 = 16π + 28π = 44π ≈ 138.23 m2. Second example, same numbers, different question: "How much air does the tent hold, if its vertical height is 5 m?" Decision: holds -> volume; cone; VERTICAL height. Execute: V = 1/3 x π x 16 x 5 = (80/3)π ≈ 83.78 m3. Same tent, two different questions, two different heights - the decision routine is what keeps them apart.

Check yourself — explain it

A problem gives a pyramid's base edge, vertical height, and slant height, and asks for the volume. The slant height is...

Paired problem — example still visible

A closed cylinder, r = 6 cm, h = 6 cm: decide, then find the SA -> SA; both terms: 2π x 36 + 2π x 6 x 6 = 72π + 72π = 144π ≈ 452.39 cm2

Faded completion — last step is yours

"Sphere, r = 2 cm - find the VOLUME: V = (4/3)π x ___ = ___π ≈ ___ cm3" -> 8; (32/3)π ≈ 33.51 cm3

Ready to practise?

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

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Grade 10 — Mathematics 10C › C10U02 Surface Area & Volume

L8 · Surface Area and Volume Clinic