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Main Idea and New Vocabulary

Key Concept: Surface Area of a Prism

Example 1: Surface Area of a Prism

Example 2: Surface Area of a Prism

Key Concept: Surface Area of a Cylinder

Example 3: Surface Area of a Cylinder

Example 4: Surface Area of a Cylinder

• Find the lateral and total surface area of prisms and cylinders.

• lateral face

• lateral surface area

• total surface area

Surface Area of a Prism

Find the lateral and total surface areas of the rectangular prism.

Begin by finding the perimeter and area of one base.

Perimeter of Base

P = 2b + 2w

P = 2(15) + 2(9) or 48

Area of Base

B = bw

B = (15)(9) or 135

Surface Area of a Prism

Answer: The lateral surface area is 336 square millimeters and the total surface area

of the prism is 606 square millimeters.

Use this information to find the lateral and total surface areas.

Lateral Surface Area

L.A. = Ph

L.A. = 48(7) or 336

Total Surface Area

S.A. = L.A. + 2B

S.A. = 336 + 2(135) or 606

A. 28 yd2; 108 yd2

B. 84 yd2; 124 yd2

C. 84 yd2; 164 yd2

D. 120 yd2; 200 yd2

Find the lateral and total surface areas of the rectangular prism.

KALEIDOSCOPE A kaleidoscope is made of stained glass in the shape of a triangular prism. The bases are equilateral triangles. Find the total surface area.

Surface Area of a Prism

Estimate S.A. = (2 + 2 + 2)10 + (1)(2) or 61 in2

The bases of the prism are triangles with side lengths of 1.5 inches, and a height of 1.3 inches. Find the perimeter and area of one base.

Perimeter of Base

P = 1.5 + 1.5 + 1.5

P = 4.5

Surface Area of a Prism

Area of Base

Use this information to find the total surface area.

S.A. = Ph + 2B Total surface area of prism

S.A. = 4.5(10) + 2(0.975) P = 4.5, h = 10, and B = 0.975

S.A. = 46.95 Simplify.

Surface Area of a Prism

Answer: The surface area is 46.95 square inches. Compare to the estimate.

A. 2,016 in2

B. 2,310 in2

C. 2,604 in2

D. 7,056 in2

FURNITURE A corner cabinet is in the shape of a triangular prism. The bases are right triangles. Find the total surface area.

Surface Area of a Cylinder

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

Since the diameter is 5 meters, the radius is 2.5 meters.

Lateral Surface Area

L.A. = 2rh

L.A. = 2(2.5)(2)

L.A. ≈ 31.4

Total Surface Area

S.A. = L.A. + 2r2

S.A. = 31.4 + 2(2.5)2

S.A. ≈ 70.7

Surface Area of a Cylinder

Answer: The lateral area is about 31.4 square meters and the surface area of the cylinder is about 70.7 square meters.

A. 219.9 cm2; 377.0 cm2

B. 439.8 cm2; 747.7 cm2

C. 1,539.4 cm2; 1,693.3 cm2

D. 1,539.4 cm2; 1,847.3 cm2

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

LABELS Find the area of the label on the can of juice. Round to the nearest tenth.

Surface Area of a Cylinder

Since the label covers the lateral surface of the can, you only need to find the can’s lateral surface area.

Estimate

L.A. = 2rh

L.A. ≈ 2(3)(2)(8) ≈ 3, r = 2.25 ≈ 2, h = 8

L.A. ≈ 96 in2

L.A. = 2rh Lateral surface area of cylinder

L.A. = 2(2.25)(8) r = 2.25, h = 8

L.A. ≈ 113.1 Simplify.

Surface Area of a Cylinder

Answer: The area of the label is about 113.1 square inches. Compare to the estimate.

A. 212.1 cm2

B. 424.1 cm2

C. 487.7 cm2

D. 551.3 cm2

LABELS Find the area of the label on the can of corn. Round to the nearest tenth.