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GEOMETRYHELP
Use a net to find the surface area of the cube.
Draw a net for the cube.
Find the area of one face. 112 = 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
Surface Areas of Prisms and CylindersLESSON 11-2
Additional Examples
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GEOMETRYHELP
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. + 2B to find the surface area of the prism. The area B of the base is ap, where a is the apothem and p is the perimeter.1
2
Draw the base.
Use 30°-60°-90° triangles to find the apothem.
The triangle has sides of length 18 cm, so p = 3 • 18 cm, or 54 cm.
Surface Areas of Prisms and CylindersLESSON 11-2
Additional Examples
![Page 3: GEOMETRY HELP 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](https://reader036.vdocuments.mx/reader036/viewer/2022083010/5697bff31a28abf838cbc64c/html5/thumbnails/3.jpg)
GEOMETRYHELP
The area of each base of the prism is 81 3 cm2.
(continued)
S.A. = L.A. + 2B Use the formula for surface area.
= ph + 2B
Rounded to the nearest whole number, the surface area is 821 cm2.
81 3B = ap =12
12 3 3 54 =
9 3 3
3 3
9 3
a = = = 3 3 Rationalize the denominator.
Surface Areas of Prisms and CylindersLESSON 11-2
Additional Examples
Quick Check
= 540 + 162 3
Use a calculator.
9 = 3 a longer leg 3 shorter leg
2(81 3 ) Substitute = (54)(10) +
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GEOMETRYHELP
S.A. = L.A. + 2B Use the formula for surface area of a cylinder.
= 2 (6)(9) + 2 (62) Substitute 6 for r and 9 for h.
The surface area of the cylinder is 180 ft2.
Quick Check
= 2 rh + Substitute the formula for lateral area of a cylinder and area of a circle.
2( r 2)
= 108 + Simplify.
= 180
72
Surface Areas of Prisms and CylindersLESSON 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 .
![Page 5: GEOMETRY HELP 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](https://reader036.vdocuments.mx/reader036/viewer/2022083010/5697bff31a28abf838cbc64c/html5/thumbnails/5.jpg)
GEOMETRYHELP
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 = .d2
S.A. = L.A. + 2B S.A. = L.A. + 2B
Cornmeal Container Barley Container
Use the formula for surface area of a
cylinder.
= 2 rh + 2 r 2 = 2 rh + 2 r 2Substitute the formulas for lateral area of a
cylinder and area of a circle.
Surface Areas of Prisms and CylindersLESSON 11-2
Additional Examples
![Page 6: GEOMETRY HELP 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](https://reader036.vdocuments.mx/reader036/viewer/2022083010/5697bff31a28abf838cbc64c/html5/thumbnails/6.jpg)
GEOMETRYHELP
Cornmeal Container Barley Container
= 32 = 42
Because 42 in.2 32 in.2, the barley container has the greater surface area.
(continued)
= (2)(6) + (22 ) = (3)(4) + (32 )Substitutefor r and h.
2 2 2 2
= 24 + = 24 + Simplify.8 18
Surface Areas of Prisms and CylindersLESSON 11-2
Additional Examples
Quick Check