Exam 18: Growth and Form

A small steel spoon is 6 inches long and weighs approximately 4 ounces. If it is used as a model for a large steel spoon to be constructed from melting approximately 200 lb of steel spoons, how long will the large spoon be?

(Multiple Choice)

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Question 21

A small steel spoon is 6 inches long and weighs approximately 4 ounces. If it is used as a model for a large steel spoon 4 feet long to be installed at the local cafe, how much would it weigh?

(Multiple Choice)

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Question 22

A dog food company sells food in cans of two sizes. A "petite" can is 4 inches tall and a "super" can is 1 foot tall. The two types of cans are geometrically similar in shape. The petite can contains 4 cents worth of metal. What is the value of the metal in the super can?

(Multiple Choice)

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Question 23

An advertisement claims that a bottle of Brand Z mouthwash is the same price as a bottle of Brand X but contains four times as much liquid as a bottle of Brand X. A bottle of Brand X mouthwash contains 12 ounces. According to the ad, how much mouthwash must a bottle of Brand Z contain?

(Multiple Choice)

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Question 24

Use the Consumer Price Index Table 21.5 to estimate when a loaf of bread, 50 cents in 1970, doubled in price.

(Short Answer)

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Question 25

Add the following measurements and give an answer with the correct number of significant digits: 1 mile, 1 foot, and 1 inch.

(Short Answer)

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Question 26

A scale model of a new building is being built for display. A scale of 1 cm to 3 m is being used. It took 27,000 square centimeters of cardboard to construct the exposed surfaces of the model. How much wood (in square meters) will be required to construct the surfaces of the building?

(Short Answer)

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Question 27

A spherical balloon has a circumference of 10 inches. If it expands so that its surface area is doubled, what happens to its volume?

(Multiple Choice)

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Question 28

Two quantities x and y show a power curve relation y = 1.24x^3.1. Using base-10 logarithmic scales for both x and y axes, the curve is transformed to a line. Find the slope of the line.

(Short Answer)

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Question 29

The weight of a block of granite 1 ft × 2 ft × 4 ft is 1320 lb. If it stands on a small face (1 ft × 2 ft), what is the pressure on the bottom face?

(Multiple Choice)

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Question 30

On a recent visit to the gym, Clark ran 3 kilometers and Bruce ran 3 miles. Who ran the farthest? How much farther (in kilometers) did he run?

(Short Answer)

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Question 31

Last summer you grew a giant squash that was 6 feet long and proportionally similar to your other squash. These squash tend to be about 1.5 feet long and weigh about 1 pound. About how much do you think the giant squash weighs?

(Multiple Choice)

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Question 32

Multiply the following measurements and give an answer with the correct number of significant digits: 3.789 m, 2.000 m, and 7.1878 m.

(Essay)

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Question 33

A wooden carving of an eagle stands 2 inches high and weighs approximately 3 ounces. If a larger carving made from the same material stands 5 feet high, how much will it weigh?

(Multiple Choice)

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Question 34

A dog food company sells food in cans of two sizes. A "petite" can is 4 inches tall and a "super" can is 1 foot tall. The two types of cans are geometrically similar in shape. What is the linear scaling factor that scales a petite can to the size of a super can?

(Multiple Choice)

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Question 35

Assume that the metabolic rate of mammals is proportional to surface area. If you scale up a cat into a supercat weighing 8 times as much, by what factor does its metabolic rate change?

(Short Answer)

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Question 36

Two quantities x and y show a power curve relation $y= 1.3 x^{-2.9}$ . Using base-10 logarithmic scales for both x and y axes, the curve is transformed to a line. Find the slope of the line.

(Multiple Choice)

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Question 37

European car makers sometimes give fuel efficiency data in liters per 100 kilometers. A Ferrari 458 Italia gets 13 liters per 100 kilometers. What is this in miles per gallon?

(Short Answer)

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Question 38

Two quantities x and y show a power curve relation y = 2.1x^1.7. Using base-10 logarithmic scales for both x and y axes, the curve is transformed to a line. Find the slope of the line.

(Multiple Choice)

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Question 39

Suppose the radius of a sphere is halved. How does the sphere's new volume compare with its former volume?

(Multiple Choice)

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Question 40

Showing 21 - 40 of 111

Exam 18: Growth and Form

A small steel spoon is 6 inches long and weighs approximately 4 ounces. If it is used as a model for a large steel spoon to be constructed from melting approximately 200 lb of steel spoons, how long will the large spoon be?

A small steel spoon is 6 inches long and weighs approximately 4 ounces. If it is used as a model for a large steel spoon 4 feet long to be installed at the local cafe, how much would it weigh?

A dog food company sells food in cans of two sizes. A "petite" can is 4 inches tall and a "super" can is 1 foot tall. The two types of cans are geometrically similar in shape. The petite can contains 4 cents worth of metal. What is the value of the metal in the super can?

An advertisement claims that a bottle of Brand Z mouthwash is the same price as a bottle of Brand X but contains four times as much liquid as a bottle of Brand X. A bottle of Brand X mouthwash contains 12 ounces. According to the ad, how much mouthwash must a bottle of Brand Z contain?

Use the Consumer Price Index Table 21.5 to estimate when a loaf of bread, 50 cents in 1970, doubled in price.

Add the following measurements and give an answer with the correct number of significant digits: 1 mile, 1 foot, and 1 inch.

A scale model of a new building is being built for display. A scale of 1 cm to 3 m is being used. It took 27,000 square centimeters of cardboard to construct the exposed surfaces of the model. How much wood (in square meters) will be required to construct the surfaces of the building?

A spherical balloon has a circumference of 10 inches. If it expands so that its surface area is doubled, what happens to its volume?

Two quantities x and y show a power curve relation y = 1.24x3.1. Using base-10 logarithmic scales for both x and y axes, the curve is transformed to a line. Find the slope of the line.

The weight of a block of granite 1 ft × 2 ft × 4 ft is 1320 lb. If it stands on a small face (1 ft × 2 ft), what is the pressure on the bottom face?

On a recent visit to the gym, Clark ran 3 kilometers and Bruce ran 3 miles. Who ran the farthest? How much farther (in kilometers) did he run?

Last summer you grew a giant squash that was 6 feet long and proportionally similar to your other squash. These squash tend to be about 1.5 feet long and weigh about 1 pound. About how much do you think the giant squash weighs?

Multiply the following measurements and give an answer with the correct number of significant digits: 3.789 m, 2.000 m, and 7.1878 m.

A wooden carving of an eagle stands 2 inches high and weighs approximately 3 ounces. If a larger carving made from the same material stands 5 feet high, how much will it weigh?

A dog food company sells food in cans of two sizes. A "petite" can is 4 inches tall and a "super" can is 1 foot tall. The two types of cans are geometrically similar in shape. What is the linear scaling factor that scales a petite can to the size of a super can?

Assume that the metabolic rate of mammals is proportional to surface area. If you scale up a cat into a supercat weighing 8 times as much, by what factor does its metabolic rate change?

Two quantities x and y show a power curve relation y=1.3x−2.9y= 1.3 x^{-2.9}y=1.3x−2.9 . Using base-10 logarithmic scales for both x and y axes, the curve is transformed to a line. Find the slope of the line.

European car makers sometimes give fuel efficiency data in liters per 100 kilometers. A Ferrari 458 Italia gets 13 liters per 100 kilometers. What is this in miles per gallon?

Two quantities x and y show a power curve relation y = 2.1x1.7. Using base-10 logarithmic scales for both x and y axes, the curve is transformed to a line. Find the slope of the line.

Suppose the radius of a sphere is halved. How does the sphere's new volume compare with its former volume?

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Two quantities x and y show a power curve relation y = 1.24x^3.1. Using base-10 logarithmic scales for both x and y axes, the curve is transformed to a line. Find the slope of the line.

Two quantities x and y show a power curve relation $y= 1.3 x^{-2.9}$ . Using base-10 logarithmic scales for both x and y axes, the curve is transformed to a line. Find the slope of the line.

Two quantities x and y show a power curve relation y = 2.1x^1.7. Using base-10 logarithmic scales for both x and y axes, the curve is transformed to a line. Find the slope of the line.