Textbook Question
Bacteria vary in size, but a diameter of 2.0 μm is not unusual. What are the volume (in cubic centimeters) and surface area (in square millimeters) of a spherical bacterium of that size?
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Ch 01: Units, Physical Quantities & Vectors
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
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Young & Freedman Calc 15th EditionCh 01: Units, Physical Quantities & VectorsProblem 11a
Young & Freedman Calc 15th EditionCh 01: Units, Physical Quantities & VectorsProblem 11aChapter 1, Problem 11a
With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is the area of the rectangle?
Verified step by step guidance1
Identify the measurements given: length = 12 mm and width = 5.98 mm.
Understand the concept of significant figures: The number of significant figures in a measurement is determined by the precision of the measuring tool used.
Determine the number of significant figures for each measurement: The length (12 mm) has 2 significant figures, and the width (5.98 mm) has 3 significant figures.
Calculate the area of the rectangle using the formula: Area = length × width. In MathML, this is represented as .
Apply the rules for significant figures in multiplication: The result should be reported with the same number of significant figures as the measurement with the least number of significant figures, which is 2 significant figures in this case.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Significant Figures
Significant figures are the digits in a measurement that contribute to its precision. They include all non-zero digits, zeros between significant digits, and trailing zeros in a decimal. When performing calculations, the result should be reported with the same number of significant figures as the measurement with the fewest significant figures.
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Measurement Precision
Measurement precision refers to the consistency and exactness of a measurement. It is determined by the instrument used and the method of measurement. In this context, the wooden ruler provides a less precise measurement (12 mm) compared to the micrometer calipers (5.98 mm), affecting the significant figures in the calculated area.
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Area Calculation
The area of a rectangle is calculated by multiplying its length by its width. In this problem, the length is 12 mm and the width is 5.98 mm. The calculation must consider significant figures, so the area should be reported with the same number of significant figures as the least precise measurement, which is 12 mm (two significant figures).
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Related Practice
Textbook Question
With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is the perimeter of the rectangle?
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Textbook Question
How many gallons of gasoline are used in the United States in one day? Assume that there are two cars for every three people, that each car is driven an average of 10,000 miles per year, and that the average car gets 20 miles per gallon.
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Textbook Question
A useful and easy-to-remember approximate value for the number of seconds in a year is π × 107. Determine the percent error in this approximate value. (There are 365.24 days in one year.)
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Textbook Question
The RDA for the trace element selenium is 0.000070 g/day. Express this dose in mg/day.
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Textbook Question
In the fall of 2002, scientists at Los Alamos National Laboratory determined that the critical mass of neptunium-237 is about 60 kg. The critical mass of a fissionable material is the minimum amount that must be brought together to start a nuclear chain reaction. Neptunium-237 has a density of 19.5 g/cm3. What would be the radius of a sphere of this material that has a critical mass?
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