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Warm Up

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Warm Up

California Standards

Lesson Presentation

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

California

Standards

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

Vocabulary

slant height

regular pyramid

right cone

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

Regular Pyramid

Right cone

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

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

1

2

= (2.4 • 2.4) + (9.6)(3)

Additional Example 1: Finding Surface Area

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

1

2

S = B + Pl

= 20.16 ft2

1

2

= (3 • 3) + (12)(5)

CheckIt Out! Example 1

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

5 m

1

2

A. S = B + Pl

3 m

= 39 m2

3 m

B. S = pr2 + prl

18 ft

= p(72) + p(7)(18)

7 ft

= 175p 549.5 ft2

Additional 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 p.

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

CheckIt Out! Example 2

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 p.

S = pr2 + pr(3l)

S = pr2 + prl

S = p(3r)2 + p(3r)l

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

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

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

= 29.25p in2 91.8 in2

= 47.25p in2 148.4 in2

= 209.25p in2 657.0 in2

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

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?

a2 + b2 = l2

Pythagorean Theorem

102 + 242 = l2

l = 26

Lateral surface area

L = prl

=p(10)(26)816.8 mm2

CheckIt 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?

a2 + b2 = l2

Pythagorean Theorem

92 + 122 = l2

l = 15

12 in.

9 in.

Lateral surface area

L = prl

=p(9)(15)424.1 in2

Lesson Quiz: Part I

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

1. the triangular pyramid

2. the cone

6.2 m2

175.8 in2

Lesson Quiz: Part II

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

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