Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

6-9 Surface and Area of Pyramids and Cones

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Warm Up

1. A rectangular prism is 0.6 m by 0.4 m by 1.0 m. What is the surface area?

2. A cylindrical can has a diameter of 14 cm and a height of 20 cm. What is the surface area to the nearest tenth? Use 3.14 for .

2.48 m2

1186.9 cm2

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Problem of the DaySandy is building a model of a pyramid with a hexagonal base. If she uses a toothpick for each edge, how many toothpicks will she need? 12

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Learn to find the surface area of pyramids and cones.

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Vocabulary

slant heightregular pyramidright cone

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

The slant height of a pyramid or cone is measured along its lateral surface.

In a right cone, a line perpendicular to the base through the tip of the cone passes through the center of the base.

The base of a regular pyramid is a regular polygon, and the lateral faces are all congruent.

Right cone

Regular Pyramid

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Additional Example 1: Finding Surface Area

Find the surface area of each figure

B. S = r2 + rl

= 20.16 ft2

= (32) + (3)(6)

= 27 84.8 cm2

A. S = B + Pl12

= (2.4 • 2.4) + (9.6)(3)12

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Try This: Example 1

Find the surface area of each figure.

= (3 • 3) + (12)(5)12

B. S = r2 + rl

= 39 m2

= (72) + (7)(18)

= 175 549.5 ft2

5 m

3 m3 m

7 ft

18 ft

A. S = B + Pl12

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Additional Example 2: Exploring the Effects of Changing Dimensions

A cone has diameter 8 in. and slant height 3 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius.

They would not have the same effect. Tripling the radius would increase the surface area more than tripling the slant height.

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Try This: Example 2

Original Dimensions Triple the Slant Height

Triple the Radius

S = r2 + rl

= (4.5)2 + (4.5)(2)

= 29.25in2 91.8 in2

S = r2 + r(3l)

= (4.5)2 + (4.5)(6)

= 47.25in2 148.4 in2

S = r)2 + r)l

= (13.5)2 + (13.5)(2)

= 209.25in2 657.0 in2

A cone has diameter 9 in. and a slant height 2 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius.

They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height.

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Additional Example 3: Application

The upper portion of an hourglass is approximately an inverted cone with the given dimensions. What is the lateral surface area of the upper portion of the hourglass?

= (10)(27.9) 876.1 mm2

Pythagorean Theorem

Lateral surface areaL = rl

a2 + b2 = l2

102 + 262 = l2

l 27.9

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Try This: Example 3

A road construction cone is almost a full cone. With the given dimensions, what is the lateral surface area of the cone?

= (4)(12.65) 158.9 in2

12 in.

4 in.

Pythagorean Theorema2 + b2 = l2

42 + 122 = l2

l 12.65Lateral surface areaL = rl

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

Lesson Quiz: Part 1

Find the surface area of each figure to the nearest tenth. Use 3.14 for .

1. the triangular pyramid

2. the cone

175.8 in2

6.2 m2

Pre-Algebra

6-9 Surface and Area of Pyramids and Cones

3. Tell whether doubling the dimensions of a cone will double the surface area.

Lesson Quiz: Part 2

Insert Lesson Title Here

It will more than double the surface area because you square the radius to find the area of the base.