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Chapter 1: Problem 55

Calculate the mass of a block of iron \(\left(d=7.86 \mathrm{g} / \mathrm{cm}^{3}\right)\) with dimensions of \(52.8 \mathrm{cm} \times 6.74 \mathrm{cm} \times 3.73 \mathrm{cm}\).

Short Answer

Expert verified
The mass of the block of iron is approximately \(8328.30 \, \mathrm{g}\).

Step by step solution

01

Calculate the Volume

We begin by calculating the volume of the iron block. The volume of a cuboid is given by the formula Volume = length * breadth * height. Plugging in the given dimensions, we get \(Volume = 52.8 \, \mathrm{cm} \times 6.74 \, \mathrm{cm} \times 3.73 \, \mathrm{cm}\).
02

Compute the Volume

After multiplying these values, the volume comes out to be \(1060.02864 \, \mathrm{cm}^{3}\).
03

Calculate the Mass

Now we use the formula Mass = Density * Volume to calculate the mass of the iron block. Substituting the density value and the calculated volume into the formula, we get \(Mass = 7.86 \, \mathrm{g/cm}^{3} \times 1060.02864 \, \mathrm{cm}^{3}\).
04

Compute the Mass

After multiplying these values, the mass comes out to be \(8328.30474 \, \mathrm{g}\), or rounded to the nearest hundredth, \(8328.30 \, \mathrm{g}\).

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Most popular questions from this chapter

The volume of seawater on Earth is about \(330,000,000 \mathrm{mi}^{3} .\) If seawater is \(3.5 \%\) sodium chloride by mass and has a density of \(1.03 \mathrm{g} / \mathrm{mL}\), what is the approximate mass of sodium chloride, in tons, dissolved in the seawater on Earth ( 1 ton \(=\) 2000 lb)?

A family/consumer science class is given an assignment in candy-making that requires a sugar mixture to be brought to a "soft-ball" stage \(\left(234-240^{\circ} \mathrm{F}\right)\). A student borrows a thermometer having a range from \(-10^{\circ} \mathrm{C}\) to \(110^{\circ} \mathrm{C}\) from the chemistry laboratory to do this assignment. Will this thermometer serve the purpose? Explain.

A pycnometer (see Exercise 78 ) weighs 25.60 g empty and \(35.55 \mathrm{g}\) when filled with water at \(20^{\circ} \mathrm{C}\) The density of water at \(20^{\circ} \mathrm{C}\) is \(0.9982 \mathrm{g} / \mathrm{mL}\). When \(10.20 \mathrm{g}\) lead is placed in the pycnometer and the pycnometer is again filled with water at \(20^{\circ} \mathrm{C}\), the total mass is \(44.83 \mathrm{g}\). What is the density of the lead in grams per cubic centimeter?

Compared with its mass on Earth, the mass of the same object on the moon should be (a) less; (b) more; (c) the same; (d) nearly the same, but somewhat less.

Calculate the mass of a cylinder of stainless steel \(\left(d=7.75 \mathrm{g} / \mathrm{cm}^{3}\right)\) with a height of \(18.35 \mathrm{cm}\) and a radius of \(1.88 \mathrm{cm}\).
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