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Amy Ferguson Moncure

7th Grade Math · Unit 8

Surface
Area

Surface area covers the outside. A rectangular prism uses 2lw + 2lh + 2wh. A right cylinder uses 2πr² + 2πrh.

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Key Ideas Easy Medium Hard
What to Remember

Prism

The surface area of a rectangular prism is 2lw + 2lh + 2wh.

That sum covers all six faces.

Cylinder

The surface area of a right cylinder is 2πr² + 2πrh.

The 2πr² covers the two circular bases. The 2πrh covers the curved side. Leave π in the answer.

Outside

Surface area covers the outside.

It is not the space inside.

Level 1

Easy

Rectangular prisms. Add the areas of the six faces.

Example
A rectangular prism is 2 in by 3 in by 4 in. Find the surface area.

SA = 2lw + 2lh + 2wh

SA = 2(2)(3) + 2(2)(4) + 2(3)(4)

SA = 2(6) + 2(8) + 2(12)

SA = 12 + 16 + 24

SA = 52

Answer: 52 square in

1
A rectangular prism is 2 in by 3 in by 5 in. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(2)(3) + 2(2)(5) + 2(3)(5)

SA = 2(6) + 2(10) + 2(15)

SA = 12 + 20 + 30

SA = 62

Answer: 62 square in

2
A rectangular prism is 2 cm by 4 cm by 6 cm. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(2)(4) + 2(2)(6) + 2(4)(6)

SA = 2(8) + 2(12) + 2(24)

SA = 16 + 24 + 48

SA = 88

Answer: 88 square cm

3
A rectangular prism is 3 in by 3 in by 3 in. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(3)(3) + 2(3)(3) + 2(3)(3)

SA = 2(9) + 2(9) + 2(9)

SA = 18 + 18 + 18

SA = 54

Answer: 54 square in

4
A rectangular prism is 1 ft by 2 ft by 3 ft. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(1)(2) + 2(1)(3) + 2(2)(3)

SA = 2(2) + 2(3) + 2(6)

SA = 4 + 6 + 12

SA = 22

Answer: 22 square ft

5
A rectangular prism is 4 in by 5 in by 6 in. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(4)(5) + 2(4)(6) + 2(5)(6)

SA = 2(20) + 2(24) + 2(30)

SA = 40 + 48 + 60

SA = 148

Answer: 148 square in

6
A rectangular prism is 3 cm by 4 cm by 5 cm. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(3)(4) + 2(3)(5) + 2(4)(5)

SA = 2(12) + 2(15) + 2(20)

SA = 24 + 30 + 40

SA = 94

Answer: 94 square cm

7
A rectangular prism is 2 in by 2 in by 5 in. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(2)(2) + 2(2)(5) + 2(2)(5)

SA = 2(4) + 2(10) + 2(10)

SA = 8 + 20 + 20

SA = 48

Answer: 48 square in

8
A rectangular prism is 1 ft by 4 ft by 8 ft. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(1)(4) + 2(1)(8) + 2(4)(8)

SA = 2(4) + 2(8) + 2(32)

SA = 8 + 16 + 64

SA = 88

Answer: 88 square ft

9
A rectangular prism is 5 cm by 5 cm by 2 cm. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(5)(5) + 2(5)(2) + 2(5)(2)

SA = 2(25) + 2(10) + 2(10)

SA = 50 + 20 + 20

SA = 90

Answer: 90 square cm

10
A rectangular prism is 3 in by 6 in by 2 in. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(3)(6) + 2(3)(2) + 2(6)(2)

SA = 2(18) + 2(6) + 2(12)

SA = 36 + 12 + 24

SA = 72

Answer: 72 square in

Level 2

Medium

Right cylinders. Leave the surface area in terms of π.

Example
A right cylinder has radius 3 cm and height 5 cm. Find the surface area in terms of π.

SA = 2πr² + 2πrh

SA = 2π3² + 2π(3)(5)

3² = 9

SA = 18π + 30π

SA = 48π

Answer: 48π square cm

1
A right cylinder has radius 2 in and height 4 in. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π2² + 2π(2)(4)

2² = 4

SA = 8π + 16π

SA = 24π

Answer: 24π square in

2
A right cylinder has radius 2 cm and height 6 cm. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π2² + 2π(2)(6)

2² = 4

SA = 8π + 24π

SA = 32π

Answer: 32π square cm

3
A right cylinder has radius 4 ft and height 3 ft. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π4² + 2π(4)(3)

4² = 16

SA = 32π + 24π

SA = 56π

Answer: 56π square ft

4
A right cylinder has radius 5 in and height 2 in. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π5² + 2π(5)(2)

5² = 25

SA = 50π + 20π

SA = 70π

Answer: 70π square in

5
A right cylinder has radius 3 cm and height 4 cm. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π3² + 2π(3)(4)

3² = 9

SA = 18π + 24π

SA = 42π

Answer: 42π square cm

6
A right cylinder has radius 4 in and height 5 in. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π4² + 2π(4)(5)

4² = 16

SA = 32π + 40π

SA = 72π

Answer: 72π square in

7
A right cylinder has radius 6 ft and height 2 ft. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π6² + 2π(6)(2)

6² = 36

SA = 72π + 24π

SA = 96π

Answer: 96π square ft

8
A right cylinder has radius 5 cm and height 5 cm. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π5² + 2π(5)(5)

5² = 25

SA = 50π + 50π

SA = 100π

Answer: 100π square cm

9
A right cylinder has radius 3 in and height 8 in. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π3² + 2π(3)(8)

3² = 9

SA = 18π + 48π

SA = 66π

Answer: 66π square in

10
A right cylinder has radius 2 ft and height 9 ft. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π2² + 2π(2)(9)

2² = 4

SA = 8π + 36π

SA = 44π

Answer: 44π square ft

Level 3

Hard

The prompt names a rectangular prism or a right cylinder. Use that formula.

Example
A rectangular prism is 9 in by 2 in by 2 in. Find the surface area.

SA = 2lw + 2lh + 2wh

SA = 2(9)(2) + 2(9)(2) + 2(2)(2)

SA = 2(18) + 2(18) + 2(4)

SA = 36 + 36 + 8

SA = 80

Answer: 80 square in

1
A rectangular prism is 4 in by 4 in by 4 in. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(4)(4) + 2(4)(4) + 2(4)(4)

SA = 2(16) + 2(16) + 2(16)

SA = 32 + 32 + 32

SA = 96

Answer: 96 square in

2
A right cylinder has radius 7 in and height 3 in. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π7² + 2π(7)(3)

7² = 49

SA = 98π + 42π

SA = 140π

Answer: 140π square in

3
A rectangular prism is 6 cm by 2 cm by 3 cm. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(6)(2) + 2(6)(3) + 2(2)(3)

SA = 2(12) + 2(18) + 2(6)

SA = 24 + 36 + 12

SA = 72

Answer: 72 square cm

4
A right cylinder has radius 8 cm and height 4 cm. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π8² + 2π(8)(4)

8² = 64

SA = 128π + 64π

SA = 192π

Answer: 192π square cm

5
A rectangular prism is 5 ft by 1 ft by 2 ft. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(5)(1) + 2(5)(2) + 2(1)(2)

SA = 2(5) + 2(10) + 2(2)

SA = 10 + 20 + 4

SA = 34

Answer: 34 square ft

6
A right cylinder has radius 9 ft and height 2 ft. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π9² + 2π(9)(2)

9² = 81

SA = 162π + 36π

SA = 198π

Answer: 198π square ft

7
A rectangular prism is 8 in by 3 in by 2 in. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(8)(3) + 2(8)(2) + 2(3)(2)

SA = 2(24) + 2(16) + 2(6)

SA = 48 + 32 + 12

SA = 92

Answer: 92 square in

8
A right cylinder has radius 4 in and height 10 in. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π4² + 2π(4)(10)

4² = 16

SA = 32π + 80π

SA = 112π

Answer: 112π square in

9
A rectangular prism is 7 cm by 4 cm by 1 cm. Find the surface area.
Show Answer

SA = 2lw + 2lh + 2wh

SA = 2(7)(4) + 2(7)(1) + 2(4)(1)

SA = 2(28) + 2(7) + 2(4)

SA = 56 + 14 + 8

SA = 78

Answer: 78 square cm

10
A right cylinder has radius 6 cm and height 6 cm. Find the surface area in terms of π.
Show Answer

SA = 2πr² + 2πrh

SA = 2π6² + 2π(6)(6)

6² = 36

SA = 72π + 72π

SA = 144π

Answer: 144π square cm

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