7.3 Volumes Of Pyramids

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English7.3SpanishVolumes of PyramidsHow can you find the volume of a pyramid?SSTATESTANDARDSMA.7.G.2.11ACTIVITY: Finding a Formula ExperimentallyWork with a partner. 2 in.2 in.2 in.Draw the two nets on cardboard and cutthem out.2 in.2 in.2.25 in.2 in.2 in.2 in.2 in.2 in.2 Fold and tape the nets to form an opensquare box and an open pyramid. Both figures should have the same size square baseand the same height. Fill the pyramid with pebbles. Then pour the pebblesinto the box. Repeat this until the box is full. Howmany pyramids does it take to fill the box? Use your result to find a formula for the volumeof a pyramid.ACTIVITY: Comparing VolumesWork with a partner. You are an archeologist studying two ancientpyramids. What factors would affect how long it took to build eachpyramid? Given similar conditions, which pyramid took longer tobuild? Explain your reasoning.Cholula Pyramid in MexicoHeight: about 217 ftBase: about 1476 ft by 1476 ft310Chapter 7Volumes of SolidsCheops Pyramid in EgyptHeight: about 480 ftBase: about 755 ft by 755 ft

EnglishSpanish3ACTIVITY: Finding and Using a PatternWork with a partner. Find the volumes of the pyramids. Organize your results in a table. Describe the pattern. Use your pattern to find the volume of a pyramid with aside length and height of 20.5432115432124ACTIVITY: Breaking a Prism into Pyramids354Work with a partner. The rectangular prism can be cut to form threepyramids. Show that the sum of the volumes of the three pyramids isequal to the volume of the prism.25a.3b.c.5. IN YOUR OWN WORDS How can you find the volume of a pyramid?6. Write a general formula for the volume of a pyramid.Use what you learned about the volumes of pyramids to completeExercises 4 – 6 on page 314.Section 7.3Volumes of Pyramids311

English7.3SpanishLessonLesson TutorialsVolume of a PyramidThe volume V of a pyramid is one-thirdthe product of the area of the base and height, hthe height of the pyramid.WordsArea of basearea of base, B13V —BhAlgebraHeight of pyramidEXAMPLE1Finding the Volume of a PyramidFind the volume of the pyramid.13Write formula for volume. —(48)(9)13Substitute. 144Multiply.V —Bh9 mmB 48 mm2The volume is 144 cubic millimeters.EXAMPLE2Finding the Volume of a PyramidFind the volume of the pyramid.Study Tipa.The area of the base ofa rectangular pyramidis the product of thelength ℓ and thewidth w.13b.7 ft4 ftYou can use V —ℓwhto find the volume of arectangular pyramid.3 ft13V —BhV —Bh13()1 13 2 —(3)(4)(7) — — (17.5)(6)(10) 28 175The volume is 28 cubic feet.Chapter 717.5 m6m1331210 mVolumes of SolidsThe volume is 175 cubicmeters.

EnglishSpanishFind the volume of the pyramid.1.Exercises 4–122.3.7 in.11 cm6 ft8 in.10 in.7 cmB 21 ftEXAMPLE18 cm2Real-Life Application3(a) How many times more sunscreen is in Bottle B than in Bottle A?(b) Which is the better buy?Bottle A 9.96a. Use the formula for the volume of a pyramid to estimate theamount of sunscreen in each bottle.Bottle B 14.40Bottle ABottle B1313V —Bh6 in.V —Bh4 in.1.5 in.1 in.2 in.133 in.13 —(2)(1)(6) —(3)(1.5)(4) 4 in.3 6 in.364So, Bottle B has —, or 1.5 times more sunscreen than Bottle A.b. Find the unit cost for each bottle.Bottle Acostvolume 9.964 in.— —3Bottle Bcostvolume 14.406 in.— —3 2.491 in. 2.401 in. —3 —3The unit cost of Bottle B is less than the unit cost of Bottle A.So, Bottle B is the better buy.Bottle CExercise 184. Bottle C is on sale for 13.20. Is Bottle Ca better buy than Bottle B in Example 3?Explain.3 in.2 in.3 in.Section 7.3Volumes of Pyramids313

EnglishSpanishExercises7.3Help with Homework1. WRITING How is the formula for the volume of a pyramid different from theformula for the volume of a prism?2. OPEN-ENDED Describe a real-life situation that involves finding the volumeof a pyramid.3. REASONING A triangular pyramid and a triangular prism have the samebase and height. How many times greater is the volume of the prism thanthe volume of the pyramid?6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Find the volume of the pyramid.124.5.6.4 mm2 ft8 yd2 ft1 ftB 15 mm24 yd7.8.5 yd9.8 in.12 mm7 cm10 in.6 in.10.3 cm11.B 63 mm21 cm15 mm7 ft8 ft6 ft14 mm20 mm12. PARACHUTE In 1483, Leonardo da Vinci designed aparachute. It is believed that this was the first parachuteever designed. In a notebook, he wrote “If a man isprovided with a length of gummed linen cloth with alength of 12 yards on each side and 12 yards high,he can jump from any great height whatsoeverwithout injury.” Find the volume of air insideLeonardo’s parachute.Not drawn to scale314Chapter 7Volumes of Solids

EnglishSpanishCopy and complete the table to find the area of the base B or theheight h of the pyramid.Volume, VArea of Base, B13.60 in.314.144 cm348 cm215.135 ft354 ft2Height,ight, h6 in.16. TEEPEE Use the photo of the teepee.a. What is the shape of the base?How can you tell?utb. The teepee’s height is aboutme10 feet. Estimate the volumeof the teepee.4 in.3 in.3 in.h17. PAPERWEIGHT How muchglass is needed to manufacture1000 paperweights? Explain your reasoning.Paperweight3 18. SPIRE Which sandcastle spire has a greatervolume? How much more sand is required to8 in.make the spire with the greater volume?6 in.B 30 in.2B 24 in.2Spire ASpire B19. OPEN-ENDED A pyramid has a volumeof 40 cubic feet and a height of 6 feet.Find one possible set of dimensions ofthe rectangular base.3z20.zDo the two solids have thesame volume? Explain.Simplify the expression.1321. — 12 7yxyxSKILLS REVIEW HANDBOOK1322. — 8 271323. — 62 51324. — 22 1525. MULTIPLE CHOICE You spend 25% of your money on a shirt. Then you spend16— of the remainder on lunch. Lunch costs 8. What percent of your money isspent on lunch?A 4.2% SECTION 4.1B 12.5% C 16.7% Section 7.3D 32% Volumes of Pyramids315

Volume of a Pyramid Words The volume V of a pyramid is one-third the product of the area of the base and the height of the pyramid. Algebra V 1 — 3 B h Height of pyramid Area of base EXAMPLE 1 Finding the Volume of a Pyramid Find the volume of the pyramid. V 1 — 3 Bh Write formula for volume. 1 — 3 (48)(9) Substitute. 144 Multiply.

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