PRE-ALGEBRA

PRE-ALGEBRA

Surface Area: Prisms and Cylinders

(10-5)What is surface area?

How do you find surface?

surface area – the sum of the areas of all of the bases and faces that make a space figure (in other words, the number of square units that would cover the \entire figure)

To find the surface area, make a net of the figure, find the area of each part of The net, and add up all the areas of the net (in other words, find the total areaof the net)

Example: Find the surface area of the following rectangular prism using a net.

1. Draw and label a net.

2. Then, find the area of each rectangle in the net.

3. Add the areas.40 + 4- + 16- + 100 + 160 + 100 = 600The surface area is 600 square in. (in. 2)

PRE-ALGEBRA

Find the surface area of the rectangular prism using a net.

60 + 60 + 150 + 90 + 150 + 90 = 600 Add the areas.

The surface area is 600 cm2.

Draw and label a net.Find the area of each rectangle in the net.

LESSON 10-5

Additional Examples

Surface Area: Prisms and Cylinders

PRE-ALGEBRA

Surface Area: Prisms and Cylinders

(10-5)What is lateral area?

How do you find lateral area?

lateral area (L.A.) – the sum of the area of the lateral (side) faces

To find the lateral area: 1. add up the areas of the side faces, or 2. Use the following formulas.

Lateral Area (L.A.) Formula (prism)

= perimeter of base (p) x height (h)

Lateral Area (L.A.) Formula (cylinder)

= Circumference of base (C) x height (h), where C = 2r

L.A.(cylinder) = C(base)h = (2r)hL.A.(cylinder) = p(base)h

PRE-ALGEBRA

Surface Area: Prisms and Cylinders

(10-5)How do you find surface area of a prism or cylinder using a formula?

Surface Area (S.A.) = Lateral Area (L.A.) + 2 Base Areas (2B)

S.A.(prism) = L.A. + 2B S.A.(cylinder) = L.A. + 2B

Example: Find the surface area of the following triangular prism. Step 1: Find the lateral area.L.A. = perimeter (p) of base height (h)

= (5 + 5 + 5) 12 = = 192

Step 2: Find the surface area.S.A. = lateral area (L.A.) + 2 base areas (2B)

= 192 + 2 (½ · 6 · 4) = 192 + 24 = 216

The surface area of the triangular prism is 216 square cm. (cm. 2)

PRE-ALGEBRA

Find the surface area of the rectangular prism.

The surface area of the rectangular prism is 500 in.2.

Step 1: Find the lateral area.

L.A. = ph Use the formula for lateral area.

= (5 + 6 + 5 + 6) 20 p = 5 + 6 + 5 + 6 and h = 20

= 440

Step 2: Find the surface area.

S.A. = L.A. + 2B Use the formula for surface area = 440 + 2(5 • 6) L.A. = 440 and B = 5 • 6 = 440 + 60 = 500

LESSON 10-5

Additional Examples

Surface Area: Prisms and Cylinders

PRE-ALGEBRA

Surface Area: Prisms and Cylinders

(10-5)Example: Find the surface area of the following sardine can to the nearest square centimeter.

Step 1: Find the lateral area. L.A. = Circumference (C = 2r) of base x height (h)

= 2r · h = 2 · 3.5 · 11.5

= 80.5 Step 2: Find the surface area. S.A. = lateral area (L.A.) + 2 base areas (2B) S.A. = L.A. + 2r2

= 80.5 + 2(3.5)2

= 80.5 + 24.5 = 105 330

The surface area of the can is 105 square cm. (cm.2 ) or about 330 square cm. (cm. 2).

PRE-ALGEBRA

Find the surface area of the cylindrical water tank.

The surface area of the water tank is about 1,156 ft2.

Step 1: Find the lateral area.

Step 2: Find the surface area.S.A. = L.A. + 2B Use the formula for surface area.

= 240 + 2(8)2

= 240 + 128 L.A. = 240 and B = (8)2

= 368 368 (3.14) Use 3.14 for . Round. 1,156

2 (8)(15)

240 r = 8 and h = 15

L.A. = 2 rh Use the formula for lateral area.

LESSON 10-5

Additional Examples

Surface Area: Prisms and Cylinders

PRE-ALGEBRA

Find the surface area of each figure rounded to the nearest whole unit.

1. triangular prism with base perimeter 24 cm, base area 24 cm2, and height 15 cm

2. rectangular prism with base perimeter 30 cm, base area 50 cm2, and height 150 cm

3. cylindrical candle with radius 2 cm and height 16 cm

about 226 cm2

408 cm2

4,600 cm2

LESSON 10-5

Surface Area: Prisms and Cylinders

Lesson Quiz