Presentation on theme: "Surface Areas of Prisms & Cylinders"— Presentation transcript:
1 Surface Areas of Prisms & Cylinders Section 11-2
2 Objectives To find the surface area of a prism To find the surface area of a cylinder
3 All About PrismsPrism - a polyhedron w/ exactly 2 congruent, parallel faces, called bases.Lateral faces - the faces that are not bases in a polyhedronNamed by the shape of its basesAltitude - perpendicular segment that joins the planes of the basesHeight (h) - length of the altitude
5 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
6 Use a net to find the surface area of the cube. Draw a net for the cube.Find the area of one face. 112 = 121The area of each face is 121 in.2.Surface Area = sum of areas of lateral faces + area of bases= ( ) + ( )= 6 • 121= 726Because there are six identical faces, the surface area is 726 in.2.
7 You tryUse a net to find the S.A. of the triangular prism
9 Use the formula L.A. = ph to find the lateral area and the formula 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 formulaS.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.12The 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.
10 9 = 3 a longer leg 3 shorter leg (continued)9 = a longer leg shorter leg9 339a = = = Rationalize the denominator.B = ap = 54 =12The area of each base of the prism is cm2.S.A. = L.A B Use the formula for surface area.= ph + 2B= (54)(10) + 2( ) Substitute=Use a calculator.Rounded to the nearest whole number, the surface area is 821 cm2.
11 You tryUse formulas to find L.A. & S.A. of the prism
13 All About Cylinders Has 2 congruent parallel bases, which are circles. Altitude - perpendicular segment that joins the planes of the basesHeight - length of the altitudeL.A. - area of resulting rectangle that can be formed by unrolling the cylinderS.A. - sum of the lateral area & area of bases
16 The radius of the base of a cylinder is 6 ft, and its height is 9 ft 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 B Use the formula for surface area of a cylinder.= rh + 2( r 2) Substitute the formula for lateral area of a cylinder and area of a circle.= (6)(9) (62) Substitute 6 for r and 9 for h.= Simplify.= 180The surface area of the cylinder is ft2.
17 You tryFind the S.A. of a cylinder with a height of 10cm and radius of 10cm in terms of pi.400cm2
18 Use the formula for surface area of a cylinder. 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 = .d2S.A. = L.A BCornmeal Container Barley ContainerUse the formula for surface area of a cylinder.= rh r 2Substitute the formulas for lateral area of a cylinder and area of a circle.
19 surface area of a cylinder. (continued)Cornmeal Container Barley ContainerS.A. = L.A BUse the formula forsurface area of a cylinder.S.A. = L.A B= rh r 2Substitute the formulas for lateral area of a cylinder and area of a circle.= rh r 2= (2)(6) (22 )= (3)(4) (32 )Substitutefor r and h.==Simplify.= 32= 42Because in.2 in.2, the barley container has the greater surface area.