(a) Three spheres of equal size are composed of aluminum (density $\left.=2.70 \mathrm{~g} / \mathrm{cm}^{3}\right),\( silver \)\left(\right.$ density \(\left.=10.49 \mathrm{~g} / \mathrm{cm}^{3}\right)\) and nickel (density \(\left.=8.90 \mathrm{~g} / \mathrm{cm}^{3}\right) .\) List the spheres from lightest to heaviest. (b) Three cubes of equal mass are composed of gold (density \(=19.32 \mathrm{~g} / \mathrm{cm}^{3}\) ), platinum (density \(\left.=21.45 \mathrm{~g} / \mathrm{cm}^{3}\right),\) and lead \(\left(\right.\) density \(\left.=11.35 \mathrm{~g} / \mathrm{cm}^{3}\right) .\) List the cubes from smallest to largest. [Section 1.5\(]\)

Short Answer

Expert verified
The short answer for the spheres lightest to heaviest is: Aluminum, Nickel, Silver. The short answer for the cubes smallest to largest is: Platinum, Gold, Lead.

Step by step solution

01

Part (a): Compare the densities of three spheres

First, list out the given densities of each sphere: Aluminum sphere: \(2.70 g/cm^3\) Silver sphere: \(10.49 g/cm^3\) Nickel sphere: \(8.90 g/cm^3\) As these spheres have the same volume, compare their densities in ascending order: 1. Aluminum sphere: \(2.70 g/cm^3\) 2. Nickel sphere: \(8.90 g/cm^3\) 3. Silver sphere: \(10.49 g/cm^3\) So, the spheres are lightest to heaviest: Aluminum, Nickel, Silver.
02

Part (b): Calculate the volumes of three cubes

Since the cubes are of equal mass, we will calculate the volumes of the cubes and compare those. We will be using the rearranged formula: Volume = Mass/Density Using the given densities: Gold cube: \(19.32 g/cm^3\) Platinum cube: \(21.45 g/cm^3\) Lead cube: \(11.35 g/cm^3\) Since the mass of the cubes is the same for all three cubes, let's call this mass M. Now, we can write the volumes of the cubes as: Gold cube volume: \(V_{gold} = \frac{M}{19.32}\) Platinum cube volume: \(V_{platinum} = \frac{M}{21.45}\) Lead cube volume: \(V_{lead} = \frac{M}{11.35}\) Comparing these volumes in ascending order, we obtain: 1. Platinum cube: \(V_{platinum} = \frac{M}{21.45}\) 2. Gold cube: \(V_{gold} = \frac{M}{19.32}\) 3. Lead cube: \(V_{lead} = \frac{M}{11.35}\) So, the cubes are smallest to largest: Platinum, Gold, Lead.

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