04.08.10 applications of volume and surface area
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The document contains 4 applications that use surface area and volume concepts: 1) Finding the height of an aquarium tank given its dimensions and volume. 2) Comparing the surface area and volume of a can and box to determine which holds more juice. 3) Calculating the surface area of a gift to see if a sheet of wrapping paper is large enough. 4) Determining which pizza sauce jar is a better buy based on price and volume.
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The document contains four applications involving calculations of surface area and volume:
1) Finding the height of an aquarium tank given its volume and base dimensions.
2) Comparing the surface area and volume of a can and box to determine which holds more juice.
3) Calculating the surface area of a gift to see if wrapping paper is large enough.
4) Determining which of two pizza sauce cans is a better buy based on volume per dollar.
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2) Comparing the surface area and volume of a can and box to determine which holds more juice.
3) Calculating the surface area of a gift to see if wrapping paper is large enough.
4) Determining which of two pizza sauce cans is a better buy based on volume per dollar.
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Lesson plan problem related to cylinder, cone, and sphere
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SURFACE AREAS AND VOLUMES OF SOLID FIGURES - MENSURATION
SURFACE AREAS AND VOLUMES OF SOLID FIGURES - MENSURATION
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Here are the steps to solve this problem:
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Solving equations with variables on both sides & translating words into symbols
Solving equations with variables on both sides & translating words into symbols
Notes on 3.2 properties of linear frunction graphs
Notes on 3.2 properties of linear frunction graphs
Simplifying expressions, solving, domain and range
Simplifying expressions, solving, domain and range
04.08.10 applications of volume and surface area
- 1. Surface Area and Volume Applications April 8, 2010
- 2. Application I A standard 20-gallon aquarium tank is a rectangular prism that holds approximately 4600 cubic inches of water. The bottom glass needs to be 24 inches by 12 inches to fit on the stand.
- 4. 4600 = (24) x (12) x h
- 5. 4600 = 288 x h
- 6. 16.0 inches = hV = 4600 cubic inches 12 inches 24 inches
- 8. TSA = 576 + 384+768
- 10. Application II Surface Area of can 9 cm 6 cm 9 cm 6 cm
- 11. Application II Surface Area of box 5 cm 9 cm 5 cm 5 cm 9 cm 5 cm
- 12. Application II Since 230cm2 > 288.2cm2, the box has a greater surface area. Which container holds more juice?
- 13. Application II Volume of can 9 cm 6 cm 9 cm 6 cm
- 14. Application II Volume of box 5 cm 9 cm 5 cm 5 cm 9 cm 5 cm
- 15. Application II Since 254.5cm3 > 225cm3, the can has greater volume. If the can and the box were the same price, which one would you buy?
- 16. Application III A birthday gift is 55 cm long, 40 cm wide, and 5 cm high. You have one sheet of wrapping paper that is 75 cm by 100 cm. Is the paper large enough to wrap the gift? Explain.
- 17. Application III TSA = 2(55)(40)+2(55)(5)+2(40)(5) TSA = 4400 + 550 + 400 TSA = 5350 sq cm A = 75 x 100 A = 7500 sq cm 100cm 5 cm 75 cm 40 cm 55 cm
- 18. Application IV If both of these cans of pizza sauce are cylinders, which is the better buy? $1.09 20.5 cm $3.49 11 cm 7.5 cm 10 cm
- 19. Application IV V = πr2h V = π(5)2(20.5) V = π * 25 * 20.5 V = 512.5 πcm3 V = 1610.1 cm3 = 461 cm3per dollar 20.5 cm $3.49 10 cm
- 20. Application IV V = πr2h V = π(3.75)2(11) V = 154.7 πcm3 V = 486.0 cm3 = 446 cm3per dollar $1.09 11 cm 7.5 cm
- 21. Application IV Which jar would you buy? Since 461 cm2 per dollar > 446 cm2 per dollar, you should buy the first jar.