Five-Minute Check (over Lesson 12–1)

Then/Now

New Vocabulary

Key Concept: Lateral Area of a Prism

Example 1: Lateral Area of a Prism

Key Concept: Surface Area of a Prism

Example 2: Surface Area of a Prism

Key Concept: Areas of a Cylinder

Example 3: Lateral Area and Surface Area of a Cylinder

Example 4: Real-World Example: Find Missing Dimensions

Over Lesson 12–1

Use isometric dot paper to sketch a cube 2 units on each edge.

A. B.

C. D.

Over Lesson 12–1

Use isometric dot paper to sketch a triangular prism 3 units high with two sides of the base that are 5 units long and 2 units long.

A. B.

C. D.

Over Lesson 12–1

Use isometric dot paper and the orthographic drawing to sketch a solid.

A. B.

C. D.

Over Lesson 12–1

A. triangle

B. rectangle

C. trapezoid

D. rhombus

Describe the cross section of a rectangular solid sliced on the diagonal.

You found areas of polygons. (Lesson 11–2)

• Find lateral areas and surface areas of prisms.

• Find lateral areas and surface areas of cylinders.

• lateral face

• lateral edge

• base edge

• altitude

• height

• lateral area

• axis

• composite solid

Lateral Area of a Prism

Find the lateral area of the regular hexagonal prism.

The bases are regular hexagons. So the perimeter of one base is 6(5) or 30 centimeters.

Answer: The lateral area is 360 square centimeters.

Lateral area of a prism

P = 30, h = 12

Multiply.

A. 162 cm2

B. 216 cm2

C. 324 cm2

D. 432 cm2

Find the lateral area of the regular octagonal prism.

Surface Area of a Prism

Find the surface area of the rectangular prism.

Surface Area of a Prism

Answer: The surface area is 360 square centimeters.

Surface area of a prism

L = Ph

Substitution

Simplify.

A. 320 units2

B. 512 units2

C. 368 units2

D. 416 units2

Find the surface area of the triangular prism.

Lateral Area and Surface Area of a Cylinder

Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.

L = 2rh Lateral area of a cylinder

= 2(14)(18) Replace r with 14 and h with 18.

≈ 1583.4 Use a calculator.

Lateral Area and Surface Area of a Cylinder

Answer: The lateral area is about 1583.4 square feet and the surface area is about 2814.9 square feet.

S = 2rh + 2r2 Surface area of a cylinder

≈ 1583.4 + 2(14)2 Replace 2rh with 1583.4

and r with 14.

≈ 2814.9 Use a calculator.

A. lateral area ≈ 1508 ft2 andsurface area ≈ 2412.7 ft2

B. lateral area ≈ 1508 ft2 andsurface area ≈ 1206.4 ft2

C. lateral area ≈ 754 ft2 andsurface area ≈ 2412.7 ft2

D. lateral area ≈ 754 ft2 andsurface area ≈ 1206.4.7 ft2

Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.

Find Missing Dimensions

MANUFACTURING A soup can is covered with the label shown. What is the radius of the soup can?

L = 2rh Lateral area of a cylinder

125.6 = 2r(8) Replace L with 15.7 ● 8 and h with 8.

125.6 = 16r Simplify.

2.5 ≈ r Divide each side by 16.

Find Missing Dimensions

Answer: The radius of the soup can is about 2.5 inches.

A. 12 inches

B. 16 inches

C. 18 inches

D. 24 inches

Find the diameter of a base of a cylinder if the surface area is 480 square inches and the height is 8 inches.