4.4 VOLUME AND SURFACE AREA
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1 160 CHAPTER 4 Geomety 4.4 VOLUME AND SURFACE AREA Textbook Refeence Section 8.4 CLAST OBJECTIVES Calculate volume and uface aea Infe fomula fo meauing geometic figue Select applicable fomula fo computing meaue of geometic figue Solve eal-wold poblem involving volume and uface aea Volume i pace occupied inide a containe. It i alway in cubic unit o unit cubed. Name Regula Sape Volume Fomula Cube ( ide ) = Rectangula Solid L W L W H H Cylinde π 2 Cone 1 2 π Spee 4 π
2 SECTION 4.4 Volume and Suface Aea 161 Example a) Find te volume. 4 m 9 m Solution Volume (V) of a cylinde = π 2 V = π (4 m) 2 (9 m) V = π 16 m 2 9 m V = 144 π m b) Find te volume of a pee of adiu 8 feet. Volume (V) of a pee = 4 π V = 4 π ( 8 ft) V = 4 π 512 ft V = V = 2048 π ft π ft c) Te volume of a cube i 125 cubic ince. Wat i te meaue of one ide? Volume (V) of a cube = V = 125 in = 125 in = 5 in = d) Find te volume of a cone of adiu millimete and eigt 5 millimete. Volume (V) of a cone = 1 π V = π ( mm) 5 mm 1 = π 9 mm 2 5 mm 1 = π 45 mm 45 = π mm = 15 π mm
3 162 CHAPTER 4 Geomety Ceck You Poge 4.4 Find te volume. 1. ½ ft 2. ½ ft ½ ft m 7.2 m 1.5 m. 2 cm 4. " 9 cm 10" 5. Find te volume of a cube of ide 5.2 ft. 6. Find te volume of a ectangula olid of lengt cm, widt 2 1 cm, and eigt of 4 cm. 7. Find te volume of a cylinde of eigt 22 ince and diamete 8 ince. 8. Find te volume of a cone of eigt 9 cm and adiu 2 cm.
4 SECTION 4.4 Volume and Suface Aea Find te volume of a pee of adiu ft. 10. A wimming pool i 12 ft wide, 20 ft long, and 8 ft deep. Wat i te volume of wate in te pool? 11. A oda can i 6 ince tall and a a adiu of ince. How muc oda i in a full can? 12. Wat i te volume of and, in cm, tat can be contained in a oe box of dimenion 10 cm by 6 cm by 18 cm? 1. A ball a adiu of 6 ince. How muc wate, in cubic ince, can te ball old? 14. A paty at i in te ape of a cone. Jane love uga. How muc uga, in cubic ince, can Jane put in e at if it i 9 ince tall wit a adiu of 2 ince? Suface Aea Suface aea i te total aea of all uface on a containe. It i alway meaued in quae unit o unit quaed. A cube a ix uface. Eac uface i a quae of imila aea. A ectangula olid a ix uface alo. o Two uface ave aea: A = L W o Two uface ave aea: A = W H o Two uface ave aea: A = L H
5 164 CHAPTER 4 Geomety Name Regula Sape Suface Aea Fomula Cube 6 ( ide ) 2 = 6 2 Rectangula Solid H L W 2 LW + 2 WH + 2 LH Example Solution e) Find te uface aea. 4.2 ft 4.2 ft Suface aea (S) of a cube = 6 2 S = 6 ( 4.2 ft) 2 S = ft 2 S = ft ft f) Find te uface aea of a box wit dimenion 10 cm by 8 cm by cm. Note tat te dimenion ae diffeent value. Ti indicate tat te box i ectangula in ape. S = 2 LW + 2 WH + 2 LH. Let H = 10 cm, W = 8 cm, and L = cm S = 2( cm 8 cm) + 2(8 cm 10 cm) + 2( cm 10 cm) S = 2(24 cm 2 ) + 2(80 cm 2 ) + 2(0 cm 2 ) S = 48 cm cm cm 2 S = 268 cm 2 Ceck You Poge 4.4 Find te volume cm cm 8.7 cm ' 10' 2'
6 SECTION 4.4 Volume and Suface Aea May want to cove a box tat meaue 20 cm by 10 cm by 5 cm. How muc pape, in q. cm., doe May need? 18. A cylindical containe can be fomed fom two top and a ectangle a own. Baed on te figue, wat i te fomula fo calculating te uface aea ( S ) of te cylinde? See If You Remembe SECTIONS Find te peimete. 2 in 1. 7 in m 6 in 1 in. Find te ditance aound a ectangle of lengt cm and widt 2 2 cm.
7 166 CHAPTER 4 Geomety 4. A cicula tack a a diamete of 50 yad. Wat i te ditance aound te tack? Find te aea of eac figue m 5 m m cm 7. 8 ft ft 8. Find te aea of a cicle of diamete 0 ince. 9. Te lengt of a elf i 28 ince, and te widt i 12 ince. How many quae feet of pape i needed to cove te elf? 10. Jan want to capet a oom tat meaue 15 feet by 12 feet. Capet i old at $10.00 pe quae yad. Wat will it cot Jan to capet te oom?
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