10-4 Surface Area of Prisms and Cylinders
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
10-4 Surface Area of Prisms and Cylinders
Warm Up
1. A triangular pyramid has a base area of 1.2 m2
and a height of 7.5 m. What is the volume of
the pyramid?
3 m3
2. A cone has a radius of 4 cm and a height of 10
cm. What is the volume of the cone to the
nearest cubic centimeter? Use 3.14 for p.
167 cm3
Holt CA Course 1
10-4 Surface Area of Prisms and Cylinders
California
Standards
MG2.1 Use formulas routinely for finding
the perimeter and area of basic twodimensional 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
Holt CA Course 1
10-4 Surface Area of Prisms and Cylinders
Vocabulary
surface area
lateral face
lateral area
lateral surface
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
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.
Draw each view of the figure.
top
front
left
1 cm
1 cm
Find the area of each
view.
12 + 8 + 6 + 12 +
8 + 6 = 52
bottom
The surface area is 52 cm2.
Holt CA Course 1
back
right
10-4 Surface Area of Prisms and Cylinders
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.
Draw each view of the figure.
top
front
left
1 cm
1 cm
Find the area of each
view.
bottom
8+8+6+8+8
+ 6 = 44
The surface area is 44 cm2.
Holt CA Course 1
back
right
10-4 Surface Area of Prisms and Cylinders
Check It Out! Example 1A
Find the surface area of each figure. The
figure is made up of congruent cubes.
Draw each view of the figure.
top
front
left
1 cm
1 cm
Find the area of each
view.
bottom
8+8+4+8+8
+ 4 = 40
The surface area is 40 cm2.
Holt CA Course 1
back
right
10-4 Surface Area of Prisms and Cylinders
Check It Out! Example 1B
Find the surface area of each figure. The
figure is made up of congruent cubes.
Draw each view of the figure.
top
front
left
1 cm
1 cm
Find the area of each
view.
bottom
8+9+6+8+9
+ 6 = 46
The surface area is 46 cm2.
Holt CA Course 1
back
right
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
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.
S = 2B + Ph
= 2( 1 • 8 • 3) + (18)(10)
2
= 204 ft2
Holt CA Course 1
10-4 Surface Area of Prisms and Cylinders
Check It Out! Example 2
Find the surface area of the figure to
the nearest tenth.
The figure is a triangular prism.
S = 2B + Ph
= 2( 1 • 7 • 6) + (21)(10)
2
= 252 cm2
Holt CA Course 1
7 cm
10 cm
7 cm
6 cm
7 cm
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
Additional Example 3: Finding Surface Area of
Cylinders
Find the surface area of the cylinder to the
nearest tenth. Use 3.14 for p.
S = 2pr2 + 2prh
= 2p(42) + 2p(4)(6)
= 80p in2  251.2 in2
Holt CA Course 1
10-4 Surface Area of Prisms and Cylinders
Check It Out! Example 3
Find the surface area of the cylinder to the
nearest tenth. Use 3.14 for p.
15 cm
S = 2pr2 + 2prh
=
2p(152)
+ 2p(15)(3)
= 540p in2  1695.6 cm2
Holt CA Course 1
3 cm
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.
The cylinder’s diameter is about 8 cm, and its
height is about 11 cm.
L = 2prh
= 2p(4)(11)
Only the lateral surface needs
to be covered.
Diameter ≈ 8 cm, so r ≈ 4 cm.
= 88p ≈ 267.3 cm2
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.
S = 2pr2 + 2prh
=
2p(32)
+ 2p(3)(12)
= 90p ft2  282.6 ft2
Holt CA Course 1
The diameter is 6 ft,
so r = 3 ft.
10-4 Surface Area of Prisms and Cylinders
Lesson Quiz
Find the surface area of each figure to the
nearest tenth. Use 3.14 for p.
1. the triangular prism 360 cm2
2. the cylinder 320.3 in2
3. All outer surfaces of a box
are covered with gold foil,
except the bottom. The box
measures 6 in. long, 4 in.
wide, and 3 in. high. How
much gold foil was used? 84 in2
Holt CA Course 1