Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples Quick Check Use a net to find the surface area of the cube. Draw a.
Download ReportTranscript Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples Quick Check Use a net to find the surface area of the cube. Draw a.
Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples
Use a net to find the surface area of the cube.
Draw a net for the cube.
Find the area of one face. 11 2 = 121 The area of each face is 121 in.
2 .
Surface Area = sum of areas of lateral faces + area of bases = (121 + 121 + 121 + 121) + (121 + 121) = 6 • 121 = 726 Because there are six identical faces, the surface area is 726 in.
2 .
Quick Check HELP GEOMETRY
Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples
Find the surface area of a 10-cm high right prism with triangular bases having 18-cm edges. Round to the nearest whole number.
Use the formula L.A. =
ph
to find the lateral area and the formula S.A. = L.A. + 2
B
base is 2
ap
to find the surface area of the prism. The area , where
a
is the apothem and
p
is the perimeter.
B
of the The triangle has sides of length 18 cm, so
p
= 3 • 18 cm, or 54 cm.
Draw the base.
Use 30 °-60°-90° triangles to find the apothem.
HELP GEOMETRY
Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples Quick Check (continued)
9 = 3
a
longer leg 3 shorter leg
a
= 9 3 3 3
=
9 3 3
=
3 3 Rationalize the denominator.
B
= 1 2
a p
= 1 2 3 3 54 = 81 3 The area of each base of the prism is 81 3 cm 2 .
S.A. = = L.A.
ph
+ 2 + 2
B B
Use the formula for surface area.
= ( 54 )( 10 ) + 2( 81 3 ) Substitute = 540 + 162 3 Use a calculator.
Rounded to the nearest whole number, the surface area is 821 cm 2 .
HELP GEOMETRY
Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples
The radius of the base of a cylinder is 6 ft, and its height is 9 ft. Find its surface area in terms of .
S.A. = L.A.
+ 2
B
Use the formula for surface area of a cylinder.
= 2
rh
Substitute the formula for lateral area of a cylinder and area of a circle.
= 2 (6)(9) + 2 (6 2 ) Substitute 6 for
r
and 9 for
h
.
Simplify.
= 180 The surface area of the cylinder is 180 ft 2 .
Quick Check HELP GEOMETRY
Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples
A company sells cornmeal and barley in cylindrical containers. The diameter of the base of the 6-in. high cornmeal container is 4 in. The diameter of the base of the 4-in. high barley container is 6 in. Which container has the greater surface area?
Find the surface area of each container. Remember that
r d
= .
2
Cornmeal Container
S.A. = L.A.
+ 2
B
Use the formula for surface area of a cylinder.
Barley Container
S.A. = L.A.
+ 2
B
= 2
rh
+ 2
r
2 Substitute the formulas for lateral area of a cylinder and area of a circle.
= 2
rh
+ 2
r
2
HELP GEOMETRY
Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples (continued)
Cornmeal Container Barley Container
= 2 (2)(6) + 2 (2 2 ) Substitute for
r
and
h
.
= 2 = 24 + 8 = 32 Simplify.
= 42 Because 42 in.
2 surface area.
32 in.
2 , the barley container has the greater (3 2 )
HELP Quick Check GEOMETRY