Grade 10 — Mathematics 10-3 › T3U04 Area & Surface Area

Grade 10 › T3U04 Area & Surface Area › L4
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-M4

L4 · Surface area of right cylinders and cones (and prisms, reviewed)

Learning goal

“I can find the surface area of a right cylinder and a right cone from their formulas - every face accounted for - and review the surface area of prisms by adding face areas. I know which faces a real job actually exposes.”

Surface area — the total area of ALL the faces of a 3-D object: the amount of material that covers it. For 3-D objects in this outcome, "area" always means surface area.
Net — the flat pattern a solid unfolds into: a cylinder's net is two circles and a rectangle; a cone's net is a circle and a sector. The formula IS the net, added up.
Slant height (s) — the distance down the SLOPE of a cone, from apex to rim - the length you would measure along the surface. It is not the vertical height.
Lateral surface — the "side" of a solid, excluding the top and bottom faces: a can's label is its lateral surface: 2πrh for a cylinder, πrs for a cone.
Worked example

A closed can has radius 5 cm and height 12 cm. Find its surface area. Step 1 (read the formula as a net): SA = 2πr² + 2πrh. The first term is the TWO circular ends; the second is the label-rectangle (length 2πr wrapped around, height h). Step 2: Ends: 2 x 3.14 x 25 = 157 cm². Side: 2 x 3.14 x 5 x 12 = 376.8 cm². Step 3: SA = 157 + 376.8 = 533.8 cm². Sanity: the side alone is bigger than the two ends together - plausible for a tall can.

Check yourself — explain it

Why does the cylinder formula have TWO terms?

Paired problem — example still visible

Closed cylinder, r = 3 cm, h = 10 cm. -> 244.92 cm² (ends 2 x 3.14 x 9 = 56.52; side 2 x 3.14 x 3 x 10 = 188.4)

Faded completion — last step is yours

"Cylinder, r = 4 cm, h = 9 cm: ends 2πr² = ___ cm²; side 2πrh = ___ cm²; SA = ___ cm²." -> 100.48; 226.08; 326.56 cm²

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