Solution Found!
Solved: Calculate the mass of each of the following: (a) a
Chapter 1, Problem 1.57(choose chapter or problem)
Calculate the mass of each of the following:
(a) a sphere of gold with a radius of 10.0 cm [the volume of a sphere with a radius r is \(V=(4 / 3) \pi r^{3}\); the density of gold = \(19.3\mathrm{\ g}/\mathrm{cm}^3\)],
(b) a cube of platinum of edge length 0.040 mm (the density of platinum = \(21.4\mathrm{\ g}/\mathrm{cm}^3\))
(c) 50.0 mL of ethanol (the density of ethanol = 0.798 g/mL).
Questions & Answers
QUESTION:
Calculate the mass of each of the following:
(a) a sphere of gold with a radius of 10.0 cm [the volume of a sphere with a radius r is \(V=(4 / 3) \pi r^{3}\); the density of gold = \(19.3\mathrm{\ g}/\mathrm{cm}^3\)],
(b) a cube of platinum of edge length 0.040 mm (the density of platinum = \(21.4\mathrm{\ g}/\mathrm{cm}^3\))
(c) 50.0 mL of ethanol (the density of ethanol = 0.798 g/mL).
ANSWER:Step 1 of 3
Here we have to calculate the mass.
It is known that \(\text { mass }=\text { density } \times \text { volume }\)
(a) a sphere of gold with a radius of 10.0 cm
In this question it has been given that,
\(\text { density }=19.3 \mathrm{~g} / \mathrm{cm}^{3}\)
\(\text { volume }=(4 / 3) \pi r^{3}\) where r is the radius = 10.0 cm
\(\begin{array}{l}
=(4 / 3) \times 3.14 \times(10)^{3} \\
=4,188 \mathrm{~cm}^{3}
\end{array}\)
\(\text { Mass }=\text { density } \times \text { volume }\)
\(\begin{array}{l}
=19.3 \mathrm{~g} / \mathrm{cm}^{3} \times 4,188 \mathrm{~cm}^{3} \\
=8.08 \times 10^{4} \mathrm{~g}
\end{array}\)
Thus the mass of the gold sphere is found to be \(8.08 \times 10^{4} \mathrm{~g}\)
