Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

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.Also covered: MG2.2, MG2.3

California Standards

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

The surface area of a three-dimensional figure is the sum of the areas of all its surfaces. You can use centimeter cubes to explore the surface area of prisms.

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

Draw each view of the figure.

Additional Example 1A: Finding Surface Area of Figures Built of Cubes

Find the surface area of each figure. The figure is made up of congruent cubes.

top front left

bottom back right

1 cm

1 cm

Find the area of each view.12 + 8 + 6 + 12 + 8 + 6 = 52

The surface area is 52 cm2.

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

Draw each view of the figure.

Additional Example 1B: Finding Surface Area of Figures Built of Cubes

Find the surface area of each figure. The figure is made up of congruent cubes.

top front left

bottom back right

1 cm

1 cm

Find the area of each view.8 + 8 + 6 + 8 + 8 + 6 = 44The surface area is 44 cm2.

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

Draw each view of the figure.

Check It Out! Example 1A

Find the surface area of each figure. The figure is made up of congruent cubes.

top front left

bottom back right

1 cm

1 cm

Find the area of each view.

8 + 8 + 4 + 8 + 8 + 4 = 40

The surface area is 40 cm2.

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

Draw each view of the figure.

Check It Out! Example 1B

Find the surface area of each figure. The figure is made up of congruent cubes.

top front left

bottom back right

1 cm

1 cm

Find the area of each view.

8 + 9 + 6 + 8 + 9 + 6 = 46

The surface area is 46 cm2.

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

The lateral faces of a prism are parallelograms that connect the bases. The lateral area of a prism is the sum of the areas of the lateral faces.

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

S = 2B + Ph

= 204 ft2

= 2( • 8 • 3) + (18)(10)12

Additional Example 2: Finding Surface Area of Prisms

Find the surface area of the figure to the nearest tenth.

The figure is a triangular prism.

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

S = 2B + Ph

= 252 cm2

= 2( • 7 • 6) + (21)(10)12

Check It Out! Example 2

7 cm7 cm

7 cm10 cm

6 cm

Find the surface area of the figure to the nearest tenth.

The figure is a triangular prism.

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

The lateral surface of a cylinder is the curved surface.

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

S = 2r2 + 2rh

= 2(42) + 2(4)(6)

= 80 in2 251.2 in2

Additional Example 3: Finding Surface Area of Cylinders

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

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

S = 2r2 + 2rh

= 2(152) + 2(15)(3)

= 540 in2 1695.6 cm2

Check It Out! Example 3

15 cm

3 cm

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

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

Additional Example 4: Application

A cylindrical soup can is 7.6 cm in diameter and 11.2 cm tall. Estimate the area of the label that covers the side of the can.

Only the lateral surface needs to be covered.

Diameter ≈ 8 cm, so r ≈ 4 cm.

L = 2rh

= 2(4)(11)

= 88 ≈ 267.3 cm2

The cylinder’s diameter is about 8 cm, and its height is about 11 cm.

Holt CA Course 1

10-4 Surface Area of Prisms and Cylinders

Check It Out! Example 4

A cylindrical storage tank that is 6 ft in diameter and 12 ft tall needs to be painted. Estimate the area to be painted.

The diameter is 6 ft, so r = 3 ft.

S = 2r2 + 2rh

= 2(32) + 2(3)(12)

= 90 ft2 282.6 ft2