Holt CA Course 1

10-5 Surface Area of Pyramids and Cones

Warm Up

California StandardsCalifornia Standards

Lesson Presentation

PreviewPreview

Holt CA Course 1

10-5 Surface 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

Holt CA Course 1

10-5 Surface Area of Pyramids and Cones

Extension of MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

California Standards

Holt CA Course 1

10-5 Surface Area of Pyramids and Cones

Vocabulary

slant heightregular pyramidright cone

Holt CA Course 1

10-5 Surface 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 vertex 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

Holt CA Course 1

10-5 Surface Area of Pyramids and Cones

Holt CA Course 1

10-5 Surface Area of Pyramids and Cones

Additional Example 1: Finding Surface AreaFind the surface area of the figure to the nearest tenth. Use 3.14 for .

= 20.16 ft2

S = B + Pl12

= (2.4 • 2.4) + (9.6)(3)12

Holt CA Course 1

10-5 Surface Area of Pyramids and Cones

Check It Out! Example 1

= (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

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

Holt CA Course 1

10-5 Surface Area of Pyramids and ConesAdditional Example 2: Exploring the Effects of Changing

Dimensions A cone has diameter 8 in. and slant height 3 in. Explain whether tripling only the slant height would have the same effect on the surface area as tripling only the radius. Use 3.14 for .

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

Holt CA Course 1

10-5 Surface Area of Pyramids and Cones

Check It Out! 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 only the slant height would have the same effect on the surface area as tripling only the radius. Use the 3.14 for .

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

Holt CA Course 1

10-5 Surface 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)(26) 816.8 mm2

Pythagorean Theorem

Lateral surface areaL = rl

a2 + b2 = l2

102 + 242 = l2

l = 26

Holt CA Course 1

10-5 Surface Area of Pyramids and Cones

Check It Out! Example 3

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

= (9)(15) 424.1 in2

12 in. 9 in.

Pythagorean Theorema2 + b2 = l2

92 + 122 = l2

l = 15Lateral surface areaL = rl

Holt CA Course 1

10-5 Surface Area of Pyramids and Cones

Lesson Quiz: Part I

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

1. the triangular pyramid

2. the cone175.8 in2

6.2 m2

Holt CA Course 1

10-5 Surface Area of Pyramids and Cones

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

Lesson Quiz: Part II

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