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Chapter 2: Problem 156

A solid metal sphere has a volume of \(4.2 \mathrm{ft}^{3}\). The mass of the sphere is 155 lb. Find the density of the metal sphere in grams per cubic centimeter.

Short Answer

Expert verified
The density of the metal sphere is approximately \(0.5910\ \frac{g}{cm^{3}}\).

Step by step solution

01

Convert volume to cubic centimeters

Given the volume of the sphere is 4.2 ft鲁. We need to convert this volume to cubic centimeters (cm鲁). We know that 1 ft = 30.48 cm. Therefore, 1 ft鲁 = (30.48 cm)鲁 = 28316.8466 cm鲁. So, the volume of the sphere in cubic centimeters is: \(4.2\ ft^{3} \times 28316.8466\frac{cm^{3}}{ft^{3}} = 118929.1557\ cm^{3}\)
02

Convert mass to grams

Given the mass of the sphere is 155 lb. We need to convert this mass to grams (g). We know that 1 lb = 453.59237 g. So, the mass of the sphere in grams is: \(155\ lb \times 453.59237\frac{g}{lb} = 70305.8172\ g\)
03

Calculate density

We have the volume and mass in the appropriate units (cm鲁 and g). Now, we can calculate the density using the formula: Density (蟻) = \( \frac{Mass}{Volume} \) \( \rho = \frac{70305.8172 g}{118929.1557 cm^{3}} = 0.5910\ \frac{g}{cm^{3}}\) The density of the metal sphere is approximately 0.5910 grams per cubic centimeter.

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Most popular questions from this chapter

A material will float on the surface of a liquid if the material has a density less than that of the liquid. Given that the density of water is approximately 1.0 g/mL under many conditions, will a block of material having a volume of \(1.2 \times 10^{4}\) in. \(^{3}\) and weighing 3.5 lb float or sink when placed in a reservoir of water?

The density of pure silver is \(10.5 \mathrm{g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C} .\) If \(5.25 \mathrm{g}\) of pure silver pellets is added to a graduated cylinder containing \(11.2 \mathrm{mL}\) of water, to what volume level will the water in the cylinder rise?

A sample containing \(33.42 \mathrm{g}\) of metal pellets is poured into a graduated cylinder initially containing 12.7 mL of water, causing the water level in the cylinder to rise to \(21.6 \mathrm{mL}\). Calculate the density of the metal.

The most common units for density are _______.

Evaluate each of the following, and write the answer to the appropriate number of significant figures. a. \(\left(2.9932 \times 10^{4}\right)\left[2.4443 \times 10^{2}+1.0032 \times 10^{1}\right]\) b. \(\left[2.34 \times 10^{2}+2.443 \times 10^{-1}\right] /(0.0323)\) c. \(\left(4.38 \times 10^{-3}\right)^{2}\) d. \(\left(5.9938 \times 10^{-6}\right)^{1 / 2}\)
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