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Directions: Read carefully and choose the best answer.. Be sure to show your work.
1.
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A thermal insulating sleeve is used to cover the lateral surface of a hot water heater to help improve efficiency. The hot water tank is a cylinder with a 13 inch radius and a 75 inch height. The sleeve is 3 inches thick.
The insulting material that makes up the sleeve is a fiberglass composite. How many cubic inches of fiberglass composite are needed to create each sleeve, to the nearest tenth of a cubic foot ? |
Not drawn to scale.
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Spheres appear in nature whenever a surface wants to be as small as possible. Soap bubbles are an example of such a surface. The diameter of the soap bubble, at the right, is 12 inches. What is the volume of air contained by this spherical bubble, to the nearest cubic inch ? |
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The Great Pyramid of Giza is the oldest and largest of the three major Egyptian pyramids. Its height is 480 feet, it contains 201 courses, and its square base measures 755 feet on each side. Find the length of the lateral edge of the pyramid, to the nearest foot. |
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In Australia, a standard size soda can holds 375 ml. In the US, a standard size soda can holds 355 ml. The US can measures 4.87 inches in height with an average diameter of 2.38 inches. Which of the choices would be the best estimate of the volume of the Australian soda can? |
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5. |
The two silos shown at the right store seed. Container C contains a preservative coating that is sprayed on the seeds as they enter the silos.
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a) It takes 10 hours to fill silos A and B with coated seed. At what rate, in cubic feet per minute, are the silos being filled?
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b) The preservative coating in container C costs $95.85 per cubic yard. One full container will treat 5,000 cubic feet of seed. How much will the preservative cost to treat all of the seeds if silos A and B are full?
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The Environmental Protection Agency is attempting to revive 3 acres of contaminated soil by replacing the top 24 inches of the soil. Trucks with a hauling capacity of 28 cubic yards of soil are hired to remove the contaminated soil. How many full truckloads of contaminated soil will be hauled away? [1 acre = 43,560 sq.ft.]
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7. |
A laboratory has 150 ml (150 cm3) bottles of nutrient agar for growing bacteria. Five petri dishes, each with a radius of 5 cm and a height of 1.4 cm are being used for an experiment.
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a) How many bottles of the agar will need to be opened to completely fill the 5 petri dishes?
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b) After one hour, the density of bacteria in petri dish A is 714 per cm3, and the density in petri dish B is 1250 per cm3. How many bacteria were present in both dishes after one hour?
Hint: Think carefully about the rounding in this problem!!!
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8. |
The trapezoidal end of a feeding trough shown below has base dimensions of 1 foot and 2 feet with a base angle of 60º. Grain is placed in the trough using a hemispherical feed scoop with a diameter of 1 foot. What is the maximum number of full scoops that can be placed into the trough without overflowing the interior of the trough? |
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A pharmacist is filling medicine capsules. The capsules are cylinders with half spheres on each end. If the length of the cylinder is 12 mm and the radius is 2 mm, how many cubic mm of medication can one capsule hold? (Round answer to the nearest tenth of a cubic mm.) |
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10. |
The Andersons have hired a landscaping firm to prepare their flower beds for the summer. They have four beds to mulch: |
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• a 10' by 25' rectangular bed
• a 8' by 25' rectangular bed
• a 4' by 25' rectangular bed
• circular bed - 18 ft. diameter.
Cedar bark mulch 6 inches deep is to be spread on each of the beds. The mulch is sold in bags containing 3 cubic feet for $6.95 per bag.
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If the landscaping company charges $200 plus the cost of the mulch, what will the Andersons pay for this mulching work? Choose:
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