6. [Suface Aea] Skill 6.1 Calculating the suface aea of ectangula pisms and cubes by using nets (1). Find any unknown side lengths. Calculate the aea of each face as shown on the net. Hint: Rectangula pisms have 6 faces of 3 diffeent sizes: base and top () font and back () othe faces () Add togethe the aea of all faces. Hints: Sides maked with a dash ( ) ae of equal length. Sides maked with two dashes ( ) ae of equal length etc. continues on page 306 Q. Find the suface aea of the cube by finding the aea of its net. 5 A. Aea of squae face = 5 units 5 units = 5 sq. units 5 6 = 150 sq. units A cube has 6 identical faces a) Find the suface aea of the ectangula pism by finding the aea of its net. b) Find the suface aea of the cube by finding the aea of its net. 30 0 F o n t Top B a c k 3 F o n t Top B a c k 6 Aea: base & top = 0 3 = 10 Aea: font & back = 30 3 = 180 Aea: othe faces = 30 0 = 100 10 + 180 + 100 =... sq. units Aea of 1 face = =... sq. units page 305 www.mathsmate.net
Skill 6.1 Calculating the suface aea of ectangula pisms and cubes by using nets (). c) Find the suface aea of the squae pism by finding the aea of its net. d) Find the suface aea of the ectangula pism by finding the aea of its net. continued fom page 305 Top 3 Back Top L a te f a ce 8 Top a l Font 1 0 5 Aea: base & top = Aea: 4 lateal faces = =... sq. units Aea: base & top = Aea: font & back = Aea: othe faces = =... sq. units e) Find the suface aea of the squae pism by finding the aea of its net. f) Find the suface aea of the ectangula pism by finding the aea of its net. 4 7 16 4 30 =... sq. units =... sq. units page 306 www.mathsmate.net
Skill 6. Calculating the suface aea of ectangula pisms. Substitute known values into the fomula: ectangula pism cube (length width) + (length height) + (width height) lw + lh + wh = (lw + lh + wh) 6(length length) = 6l l h w Q. Lewis wants to make a box, with a lid, fo his cad collection. The box needs a base of 11 cm by 0 cm and must be 1 cm high. How much wood does Lewis need? a) The locke block needs to be esufaced. What is the suface aea of this ectangula pism disegading its base? A. (lw + lh + wh) whee l = 0, w = 11 and h = 1 = (0 + 0 1 + 11 1) = (0 + 40 + 13) = 59 = 1184 b) Zoe s mattess was ton in emoval. What is the minimum amount of mattess ticking needed to e-cove the mattess? 1.5 yd Subtact 1 base aea 55 cm lw + lh + wh whee l = 110, w = 55 and h = 190 = 110 55 + (110 190) + (55 190) = 6050 + 0,900 + 10,450 = 6050 + 41,800 + 0,900 = 110 cm 190 cm yd 0.5 yd (lw + lh + wh) = = yd c) Find the suface aea of the micowave. 30 cm d) The suface aea of the ectangula pism is 5 squae inches. What is the S.A. if all the dimensions ae doubled? 4 in. in. 50 cm 35 cm 3 in. = = = = page 307 www.mathsmate.net
Skill 6.3 Calculating the suface aea of ectangula composite solids (1). Find any unknown side lengths. Calculate the aea of each face. Add togethe the aea of all faces. OR Identify the base by finding the two, identical paallel faces. Hint: A pism does not necessaily sit on its base. Substitute values into the fomula: continues on page 309 ectangula composite solid Peimete of base height + Aea of base Ph + B h Q. Find the suface aea of the pism. A. 1 in. OR 6 in. 1 in. 6 + 1 + 5 + 1 + 1 + = 16 6 + 6 + + = 16 1 in. 5 in. 5 in. base 6 in. base 6 in. 1 in. in. h = in. in. B = 5 1 + 1 = 5 + = 7 Ph + B whee h = = 16 + 7 = 3 + 14 = 46 Fo P, convet to a ectangle Find unknown side lengths a) Find the suface aea of the pism. 3 cm Fo P, convet to a ectangle Fo B, find all unknown side lengths b) Find the suface aea of the pism. 7 ft 10 cm 10 cm 5 cm 5 cm 5 cm 10 ft 10 + 10 + 8 + 8 = 36 B = 5 5 + 5 8 = 5 + 40 = 65 Ph + B whee h = 3 = 36 3 + 65 = 108 + 130 = B = Ph + B = ft page 308 www.mathsmate.net
Skill 6.3 Calculating the suface aea of ectangula composite solids (). c) Find the suface aea of the pism. 10 m Find unknown side lengths d) Find the suface aea of the pism. 6 yd 4 yd 3 yd continued fom page 308 4 m B = Ph + B whee h = yd B = Ph + B = = m yd e) A window m by 1.5 m and a dooway m by 0.8 m ae in the plan fo this oom. Find the aea of the walls to be painted. 5 m f) Find the suface aea of the pism. 4 m 3 m 9 in. = g) Find the suface aea of the pism. 40 ft 10 ft m = h) Find the suface aea of the pism. 5 cm 3 cm 1 = ft = page 309 www.mathsmate.net
Skill 6.4 Calculating the suface aea of tiangula pisms (1). Find any unknown side lengths. Calculate the aea of each face. Add togethe the aea of all faces. OR Substitute values into the fomula: continues on page 311 tiangula pism Peimete of base height + Aea of base Ph + B h Hint: Do not confuse the height needed to calculate the aea of the tiangula base, with the height (h) of the pism. Q. Find the suface aea of the tiangula pism. A. 6 + 5 + 5 = 16 1 6 cm B = bh whee b = 6, h = 4 4 cm 1 7 cm = (6 4) = 1 5 cm Ph + B whee h = 7 = 16 7 + 1 = 11 + 4 = 136 b h a) Find the suface aea of the tiangula pism. b) Find the suface aea of the tiangula pism. 8 in. 3 in. 5 cm 6 in. 10 in. 1 cm 1 + 1 + 1 = 36 1 A = (1 8) = 48 Ph + B whee h = 5 = 36 5 + 48 = 900 + 96 = Fist find the peimete of base Then find the aea of base A = = page 310 www.mathsmate.net
Skill 6.4 Calculating the suface aea of tiangula pisms (). c) Find the suface aea of the tiangula pism. 5 mm 0 mm d) Find the suface aea of the tiangula pism of cheese. in. 3 in. continued fom page 310 1 mm 1 in. 16 mm.5 in. B = Ph + B whee h = B = = = mm e) Find the suface aea of the tiangula pism. f) Find the suface aea of the tiangula pism. 10 in. 5 ft 5 ft 8 in. 6 in. 6.5 ft 6 in. 6 ft B = B = = = ft page 311 www.mathsmate.net
Skill 6.5 Calculating the suface aea of pyamids (1). Find any unknown side lengths. Calculate the aea of each face. Add togethe the aea of all faces. OR Substitute values into the fomula: egula squae pyamid Aea of base + 4 Aea of tiangle 1 B + 4 ls l + ls l continues on page 313 s l egula tiangula pyamid (egula tetahedon) 4 Aea of equilateal tiangle 1 x 3 4 x x 3 x x 3 ectangula pyamid Aea of base + Aea of tiangles left & ight + Aea of tiangles font & back 1 1 B + ws 1 + ls s 1 s lw + ws 1 + ls l w Q. Find the suface aea of the egula squae pyamid. 8 ft 1 ft a) Find the suface aea of the egula squae pyamid. 5 in. A. l + ls whee l = 8 and s = 1 = 8 8 + 8 1 = 64 + 16 1 = 64 + 19 = 56 ft b) Find the suface aea of one of the salt and peppe shakes given that they ae egula, squae pyamids of base side length 3 cm and slant height 4 cm. 6 in. l + ls whee l = 5 and s = 6 = 5 5 + 5 6 = 5 + 60 = l + ls = page 31 www.mathsmate.net
Skill 6.5 Calculating the suface aea of pyamids (). c) Find the suface aea of the lagest egula squae pyamid, which has a base side length of 00 m and slant height of 50 m. continued fom page 31 d) Find the suface aea of the egula squae pyamid. 18 mm 1 mm = m = mm e) Find the suface aea of the egula squae pyamid. f) Find the suface aea of the ectangula pyamid. 64 ft 40 ft 64 ft 15 in. 40 in. 14 in.4 in. = ft = g) Find the suface aea of the egula tetahedon. [Give you answe as a adical.] h) Find the suface aea of the egula tetahedon. [Give you answe as a adical.] 3 3 cm 1 ft 6 cm = = ft page 313 www.mathsmate.net
Skill 6.6 Calculating the suface aea of composite solids (1). Beak the solid into wokable pats. Substitute values into the appopiate fomula fo suface aea. (see skills 6. to 6.5, pages 307 to 31) continues on page 315 Q. Find the total suface aea of the obelisk. A. S.A. egula squae pyamid (without base) = ls whee l = 8 and s = 10 10 mm 8 mm = 8 10 = 160 S.A. squae pism (without base) 15 mm = 4lh + l whee l = 8 and h = 15 = 4 (8 15) + 8 8 = 4 10 + 64 = 544 S.A. obelisk = 160 + 544 = 704 mm a) Find the suface aea of the solid. 1 36, B = (10 1) = 60 and h = 10 S.A. pism = Ph + B = 36 10 + 60 = 480 S.A. pism face = 480 100 = 380 S.A. cube face = 5l = 5 100 = 500 S.A. solid = 380 + 500 = m c) Find the suface aea of the glasshouse, excluding its base. 4 m h = 10 (height) Find S.A. of the cube without the top face 6 m 13 m 1 m Find S.A. of the tiangula pism without the face that sits on the cube 10 m 0 m l = 10 (height) 5 m 5 m b) Find the suface aea of the solid. 8 in. 15 in. 17 in. = d) Find the suface aea of the obelisk. 10 yd 4 yd 5 yd = m = yd page 314 www.mathsmate.net
Skill 6.6 Calculating the suface aea of composite solids (). e) Find the suface aea of the octahedon. f) Find the suface aea of the solid. continued fom page 314 18 ft 13 cm 1 cm 10 ft 17 cm = ft = g) Lou bought a ectangula box containing 15 tightly packaged eases. What is the suface aea of the box? h) Find the suface aea of the pism. 10 in. 5 in. cm 4 cm 10 cm 4 in. in. 10 in. = = page 315 www.mathsmate.net
Skill 6.7 Calculating the suface aea of basic thee-dimensional ound solids (1). Substitute values into the fomula: continues on page 317 cylinde L.A. = πh B + L.A. = π + πh = π ( + h) h π h cone sphee L.A. = πs B + L.A. 4π s = π + πs = π ( + s) Q. Using π ( + h) and π 3.14, find the suface aea of the cyclinde. 4 cm A. π ( + h) whee = and h = 8 = 3.14 ( + 8) = 1.56 10 = 15.6 a) Use π ( + s) and π 3.14 to find the suface aea of the conical caot. b) Using 4π and π, find the 7 suface aea of the sphee. 4 cm 10 cm 1 ft π( + s) whee =, s = 10 3.14 ( + 10) = 6.8 1 = ft page 316 www.mathsmate.net
continued fom page 316 MMMauve 11 Skill 6.7 Calculating the suface aea of basic thee-dimensional MMLime 11 ound solids (). c) Using 4π and π, find the d) Use π ( + s) and π 3.14 to find how 7 suface aea of the snow globe. much aea still needs to be coveed 6 cm in chocolate to cove the whole cone given that 40 have been coveed so fa. 140 mm 33 44 33 44 1 cm mm e) Using π ( + h) and π 3.14, find the suface aea of the cyclindical stool seat. 40 cm 5 cm f) Using π ( + h) and π, find the 7 suface aea of the can of tuna. 14 cm g) Use π 3.14 to find the suface aea of the cone. [Hint: Pythagoean theoem will help.] h) Use π 3.14 to find the suface aea of the cone. [Hint: Pythagoean theoem will help.] 4 in. 10 in. 4 yd 36 yd yd page 317 www.mathsmate.net
Skill 6.8 Calculating the suface aea of moe complex thee-dimensional ound solids. Substitute values into the appopiate fomula: (see skills 6. to 6.7, pages 307 to 316) Adapt the fomula whee necessay. hemisphee 4π +π = 3π Q. Using π find the suface aea of the 7 hemisphee. 14 in. A. 3π whee = 7 1 = 3 7 7 1 7 = 66 7 = 46 a) Using π 3.14 find the suface aea of the hemisphee. b) Using π 3.14 find the suface aea of the watemelon half. 10 in. 4 ft 3π whee = 4 = 3 3.14 4 4 = 9.4 16 = 150.7 ft c) Use π 3.14 to find the suface aea of the shape. d) Use π to find the suface aea of the shape. 7 8 in. 5 ft 6 ft 10 ft S.A. pism = 0 in. 14 in. L.A. cone = = S.A. cylinde half = = S.A. cylinde = = = = ft = page 318 www.mathsmate.net
Skill 6.9 Expessing the suface aea of thee-dimensional solids in algebaic fom. Substitute values into the appopiate fomula fo suface aea. (see skills 6. to 6.8, pages 307 to 318) Adapt the fomula whee necessay. Q. Wite a fomula fo the suface aea of the cone. A. π( + s) whee = a and s = 4a = π a (a + 4a) = πa 5a = 5πa a 4a a) Wite a fomula fo the suface aea S.A. of the cylinde. b) Wite a fomula fo the suface aea S.A. of the hemisphee. 5d d π( + h) whee = d and h = 5d = πd(d + 5d) = πd 6d... = 1πd =... c) Wite a fomula fo the suface aea S.A. of the obelisk. d) Wite a fomula fo the suface aea S.A. of the cube. a 3d = = =... =... e) Wite a fomula fo the suface aea S.A. of the cylinde. 6x 10x f) Wite a fomula fo the suface aea S.A. of the cone. 7p p = = =... =... page 319 www.mathsmate.net