Surface Areas of Prisms & Cylinders
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Transcript of Surface Areas of Prisms & Cylinders
Surface Areas of Prisms & Cylinders
Section 11-2
Objectives• To find the surface area of a prism• To find the surface area of a
cylinder
All About Prisms• Prism - a polyhedron w/ exactly 2
congruent, parallel faces, called bases.• Lateral faces - the faces that are not
bases in a polyhedron• Named by the shape of its bases• Altitude - perpendicular segment that
joins the planes of the bases• Height (h) - length of the altitude
Vocab Ctd.• Lateral area - the sum of the areas
of the lateral faces• Surface area - the sum of the
lateral area and area of the two bases
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.
You try• Use a net to find the S.A. of the
triangular prism
Formulas
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
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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.
9 = 3 a longer leg 3 shorter leg
B = ap = 3 3 54 = 81 312
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The area of each base of the prism is 81 3 cm2.
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S.A. = L.A. + 2B Use the formula for surface area. = ph + 2B
= (54)(10) + 2(81 3 ) Substitute
= 540 + 162 3 820.59223 Use a calculator.Rounded to the nearest whole number, the surface area is 821 cm2.
9 3 3
3 3
9 3a = = = 3 3 Rationalize the denominator.
You try• Use formulas to find L.A. & S.A. of
the prism
All About Cylinders• Has 2 congruent parallel bases, which
are circles.• Altitude - perpendicular segment that
joins the planes of the bases• Height - length of the altitude• L.A. - area of resulting rectangle that
can be formed by unrolling the cylinder• S.A. - sum of the lateral area & area of
bases
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. + 2B Use the formula for surface area of a cylinder.
= 2 rh + 2( r 2) Substitute the formula for lateral area of a cylinder and area of a circle.
= 2 (6)(9) + 2 (62) Substitute 6 for r and 9 for h.
= 108 + 72 Simplify.
= 180
The surface area of the cylinder is 180 ft2.
You try• Find the S.A. of a cylinder with a
height of 10cm and radius of 10cm in terms of pi.
• 400cm2
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. + 2BCornmeal 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.
S.A. = L.A. + 2B S.A. = L.A. + 2BCornmeal Container Barley Container
Use the formula forsurface 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.
= 2 (2)(6) + 2 (22 ) = 2 (3)(4) + 2 (32 )Substitutefor r and h.
= 24 + 8 = 24 + 18Simplify.
= 32 = 42
Because 42 in.2 32 in.2, the barley container has the greater surface area.
(continued)