PRE-ALGEBRA

PRE-ALGEBRA

Surface Area: Pyramids, Cones, and Spheres (10-6)

How can you find the surface area of a pyramid using a formula?

Surface Area (S.A.) of a Pyramis Formula

S.A. (pyramid) = L.A. + B

where the L.A. (lateral area) = ½ · perimer of base · slant height (L.A. = ½pl) and B is the area of the Base

PRE-ALGEBRA

Surface Area: Pyramids, Cones, and Spheres (10-6)

Example: Find the surface area of the following pyramid.Method 1: Formula MethodStep 1: Find the lateral area.L.A. = ½pl (½ · perimeter of base · slant height) = ½ (12 + 12 + 12 + 12 )(16) = ½ (48) (16) = ½ (768) = 384

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

= 384 + 122

= 384 + 144 = 528

Method 2: Net MethodAdd the areas of the base and the triangles that make the pyramidArea of triangular face = ½bh (½ · base · height) = ½(12)(16) = 96Area of base = lw (length · width) = 122 = 144Area of base + area of each face = 144 + 96(4) = 144 + 384 = 528

The surface area of the square pyramid is 528 square cm. (cm. 2)

PRE-ALGEBRA

Find the surface area of the square pyramid.

The surface area of the pyramid is 105 m2.

Step 1 L.A. = p Use the formula for lateral area.12

= • 20 • 8 = 80 p = 4(5) and = 8.12

Step 2 S.A. = L.A. + B Use the formula for surface area. = 80 + 52 Lateral area = 80 and B = 52. = 80 + 25 = 105

Surface Area: Pyramids Cones and SpheresLESSON 10-6

Additional Examples

PRE-ALGEBRA

Surface Area: Pyramids, Cones, and Spheres (10-6)

How can you find the surface area of a cone using a formula?

Surface Area (S.A.) of a Cone Formula

S.A. (cone) = L.A. + B

where the L.A. (lateral area) = ½ · perimer of base · slant height (L.A. = ½pl) and B is the area of the Base

PRE-ALGEBRA

Surface Area: Pyramids, Cones, and Spheres (10-6)

Example: Find the surface area of the following cone.  Method 1: Formula MethodStep 1: Find the lateral area.L.A. = rl ( · radius of base · slant height) = (4)(10) = ½(768) = 40 Step 2: Find the surface area.S.A. = lateral area (L.A.) + area of base (B)

= 40 + r2

= 40 + (4)2

= 40 + 16 = 56 16 (3.14) 176

 Method 2: Net MethodAdd the areas of the base and the cone itselfArea of cone face = ½Ch (½ · Circumference of bottom · height) = ½(2r)h = ½(2)()(4)(10) = 40Area of base = r2 = (4)2 = 16Area of base + area of the face = 16= 40 = 56 16 (3.14) 176

The surface area of the cone is 56 square cm. (cm. 2) or about 176 square cm. (cm. 2)

PRE-ALGEBRA

Find the surface area of the cone.

The surface area of the cone is about 94 m2.

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

21 + (3)2 L.A. = 21 and B = (3)2.

= 30

= 94.2 Use 3.14 for .

Surface Area: Pyramids Cones and SpheresLESSON 10-6

Additional Examples

Step 1 L.A. = r Use the formula for lateral area.

(3)(7) r = 3 and = 7.

= 21

PRE-ALGEBRA

Surface Area: Pyramids, Cones, and Spheres (10-6)

How can you find the surface area of a sphere using a formula?

Surface Area (S.A.) of a Sphere Formula

S.A. (sphere) = .4r2

Example: Find the surface area of the following basketball.

S.A.(sphere) = 4r2 (4 · radius2) r = ½ diameter = ½ (10) = 5 = 4 (5)2 = 4 (25) = 100 100 (3.14) 314

The surface area of the sphere is 100 square in. (in. 2) or about 314 square in. (in. 2)

PRE-ALGEBRA

Earth has an average radius of 3,963 mi. What is Earth’s approximate surface area to the nearest 1,000 mi2? Assume that Earth is a sphere.

The surface area of Earth is about 197,259,000 mi2.

S.A. = 4 r 2 Use the formula for surface area.

197,259,435

= 62,821,476

= 4 (3,963)2 r 3,963 (“average” is not an exact number)

Surface Area: Pyramids Cones and SpheresLESSON 10-6

Additional Examples

PRE-ALGEBRA

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

1. a square pyramid with base edge 80 m and slant height 100 m

2. a cone with slant height 22 cm and radius 7 cm

3. a sphere with radius 12 cm

about 1,809 cm2

22,400 m2

about 637 cm2

Surface Area: Pyramids Cones and SpheresLESSON 10-6

Lesson Quiz