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Ch 01: Units, Physical Quantities & Vectors
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경
1장, 문제 13

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?

검증된 단계별 안내
1
First, understand that the bacterium is modeled as a sphere with a diameter of 2.0 μm. Convert the diameter to radius by dividing by 2, giving a radius of 1.0 μm.
Convert the radius from micrometers to centimeters for volume calculation. Since 1 μm = 1 × 10⁻⁴ cm, the radius in centimeters is 1.0 × 10⁻⁴ cm.
Use the formula for the volume of a sphere: V = (4/3)πr³. Substitute the radius in centimeters into this formula to find the volume in cubic centimeters.
Convert the radius from micrometers to millimeters for surface area calculation. Since 1 μm = 0.001 mm, the radius in millimeters is 1.0 mm.
Use the formula for the surface area of a sphere: A = 4πr². Substitute the radius in millimeters into this formula to find the surface area in square millimeters.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m
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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Volume of a Sphere

The volume of a sphere is calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. This formula helps determine the amount of space occupied by the sphere. For a bacterium with a diameter of 2.0μm, the radius is half of the diameter, which is 1.0μm, and must be converted to centimeters for the calculation.
추천 영상:
05:21
Volume Thermal Expansion

Surface Area of a Sphere

The surface area of a sphere is given by the formula A = 4πr², where r is the radius. This formula calculates the total area covering the sphere's surface. For a bacterium with a diameter of 2.0μm, the radius is 1.0μm, and it should be converted to millimeters to find the surface area in square millimeters.
추천 영상:
09:18
Equipotential Surfaces

Unit Conversion

Unit conversion is essential for solving physics problems involving measurements. In this context, converting micrometers to centimeters and millimeters is necessary to ensure the calculations are in the correct units. 1μm equals 0.0001cm and 0.001mm, which allows for accurate computation of volume and surface area in the desired units.
추천 영상:
07:46
Unit Conversions
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