Surface area | Year 11 | Ascent Library

01 / LEARN

The idea, step by step

Understand the idea

Surface area totals the surfaces specified by the problem. A closed cuboid has three matching pairs of rectangular faces; an open box does not have a top. A net makes the face count visible.

A cylinder unrolls to a rectangle whose length is the base circumference and whose width is the height. Its curved area is $2 π r h$ , and each circular end adds $π r^{2}$ .

Choose and apply a method

Decide what is exposed, painted or covered before using a formula. Joined internal faces of a composite object are not exposed. Convert the dimensions to one unit first.

Keep surface area in square units. Check whether the context includes the base, the top, or both. A volume formula cannot calculate the amount of wrapping or paint.

S A_{cuboid} = 2 (l w + l h + w h), S A_{closed cylinder} = 2 π r^{2} + 2 π r h

A common trap

Including two circular ends in the material area of an open-top tank.

Instead: List the required surfaces first; an open top contributes no material.

02 / WORKED EXAMPLES

See the thinking

Example 1

Cover a cuboid

Find surface area of a closed cuboid 6 cm by 4 cm by 3 cm.

Paired face areas are 24, 18 and 12 cm $2$ .
$S A = 2 (24 + 18 + 12) = 108$ cm $2$ .

108 cm

2

Example 2

Open cylinder

A cylindrical tank has radius 2 m and height 5 m. Find the inside base and wall area, excluding the open top.

Base area $= π {(2)}^{2} = 4 π$ .
Wall area $= 2 π (2) (5) = 20 π$ .
Total $= 24 π$ m $2$ .

24 π

2

, approximately 75.40 m

2

Check your understanding

Find the surface area of a cube of side 4 cm.

Show answer

96 cm $2$ .

There are six square faces: $6 \times 4^{2} = 96$ .

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find surface area of a cube with side 5 cm.
2 marks
Find surface area of a closed 8 cm by 3 cm by 2 cm cuboid.
2 marks
An open rectangular box has base 10 cm by 6 cm and height 4 cm. Find its material area.
2 marks
Find curved surface area of a cylinder with radius 3 cm and height 7 cm. Give an exact answer.
2 marks
Find total surface area of a closed cylinder with radius 3 cm and height 7 cm.
2 marks
Two cubes, each of side 2 cm, are joined face-to-face. Find exposed area.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find surface area of a cube with side 5 cm.
2 marks
$6 \times 5^{2} = 150$ .
150 cm $2$ .
Find surface area of a closed 8 cm by 3 cm by 2 cm cuboid.
2 marks
$2 (24 + 16 + 6) = 92$ .
92 cm $2$ .
An open rectangular box has base 10 cm by 6 cm and height 4 cm. Find its material area.
2 marks
$60 + 2 (40) + 2 (24) = 188$ .
188 cm $2$ .
Find curved surface area of a cylinder with radius 3 cm and height 7 cm. Give an exact answer.
2 marks
$2 π (3) (7) = 42 π$ .
$42 π$ cm $2$ .
Find total surface area of a closed cylinder with radius 3 cm and height 7 cm.
2 marks
$2 π {(3)}^{2} + 2 π (3) (7) = 18 π + 42 π = 60 π$ .
$60 π$ cm $2$ .
Two cubes, each of side 2 cm, are joined face-to-face. Find exposed area.
2 marks
Separate area $= 2 \times 6 \times 2^{2} = 48$ .
Two hidden joining faces total $2 \times 2^{2} = 8$ .
Exposed area $= 48 - 8 = 40$ cm $2$ .
40 cm $2$ .

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics measurement skills and applications; original explanatory lessons and papers.

Official curriculum source ↗

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