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

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.

9 = 3 a longer leg 3 shorter leg

B = ap = 3 3 54 = 81 312

12

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

= (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)