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Ch.1 - Introduction: Matter, Energy, and Measurement
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Brown 14th EditionCh.1 - Introduction: Matter, Energy, and Measurement문제 83
1장, 문제 83

A thief plans to steal a cylindrical platinum medal with a radius of 2.3 cm and a thickness of 0.8 cm from a jewellery store. If the platinum has a density of 21.45 g/cm³, what is the mass of the medal in kg? [The volume of a cylinder is V = πr²h.]

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Calculate the volume of the cylindrical medal using the formula for the volume of a cylinder: \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the thickness.
Substitute the given values into the volume formula: \( r = 2.3 \text{ cm} \) and \( h = 0.8 \text{ cm} \).
Compute the volume \( V \) in cubic centimeters (cm³) using the substituted values.
Use the density formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \) to find the mass. Rearrange it to \( \text{Mass} = \text{Density} \times \text{Volume} \).
Substitute the calculated volume and the given density (21.45 g/cm³) into the mass formula to find the mass in grams, then convert the mass from grams to kilograms by dividing by 1000.

주요 개념

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

Volume of a Cylinder

The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height (or thickness). This formula derives from the area of the circular base (πr²) multiplied by the height, providing a measure of the three-dimensional space the cylinder occupies.
추천 영상:
가이드 코스
02:35
Constant-Volume Calorimetry

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³). It indicates how much mass is contained in a given volume of a substance. In this case, the density of platinum is crucial for converting the calculated volume of the medal into mass.
추천 영상:
가이드 코스
01:56
Density Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this problem, after calculating the mass of the platinum medal in grams, it is necessary to convert this value to kilograms, as 1 kg equals 1000 g. This step ensures that the final answer is in the desired unit of measurement.
추천 영상:
가이드 코스
01:56
Conversion Factors
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