Textbook Question
Two spheres of equal volume are placed on the scales as shown. a. Which one is more dense?
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Ch.1 - Introduction: Matter, Energy, and Measurement
Chapter 1, Problem 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.]
Verified step by step guidance1
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.
Related Practice
Textbook Question
Water has a density of 0.997 g/cm3 at 25 °C; ice has a density of 0.917 g/cm3 at -10 °C. (a) If a soft-drink bottle whose volume is 1.50 L is completely filled with water and then frozen to -10 °C, what volume does the ice occupy? (b) Can the ice be contained within the bottle?
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Textbook Question
A 32.65-g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.00 mL. The solid and toluene together weigh 58.58 g. The density of toluene at the temperature of the experiment is 0.864 g/mL. What is the density of the solid?
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Textbook Question
Saline solution used in hospital contains 0.9% sodium chloride by mass. Calculate the number of grams of sodium chloride in 0.5 gal of saline solution if the solution has a density of 1.01 g/mL.
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Textbook Question
A 40-lb container of peat moss measures 14 * 20 * 30 in. A
40-lb container of topsoil has a volume of 1.9 gal. (b) How many bags of peat moss are needed to
cover an area measuring 15.0 ft * 20.0 ft to a depth of 3.0 in.?
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Open Question
A 10.0 g block of gold is hammered into a thin gold sheet which has an area of 150 cm2. Given the density of gold is 19.3 g/cm3, what is the approximate thickness of the gold sheet in millimeters?