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Chapter 1: Problem 56

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 \(1.88 \mathrm{cm}\).

Short Answer

Expert verified
To find the mass, calculate the volume of the given cylinder first and then multiply it with the density to find the mass.

Step by step solution

01

Determine the Volume

The volume of a cylinder is given by the formula \(V = \pi \times r^2 \times h\). In this case, \(r = 1.88 cm\) and \(h = 18.35 cm\). Therefore we sub these values in to calculate the volume: \(V = 3.14 \times (1.88cm)^2 \times 18.35cm\).
02

Calculate the Mass

Now, the mass of the cylinder can be calculated using the formula \(m = d \times V\). Here, \(d = 7.75g/cm^3\) and \(V\) is the value calculated in step 1. Substituting these values we can calculate the mass of the cylinder.

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Most popular questions from this chapter

The density of aluminum is \(2.70 \mathrm{g} / \mathrm{cm}^{3} .\) A square piece of aluminum foil, \(22.86 \mathrm{cm}\) on a side is found to weigh 2.568 g. What is the thickness of the foil, in millimeters?

State whether the following properties are physical or chemical. (a) A piece of sliced apple turns brown. (b) A slab of marble feels cool to the touch. (c) A sapphire is blue. (d) A clay pot fired in a kiln becomes hard and covered by a glaze.

Describe the necessary characteristics of a scientific theory.

In the third century \(\mathrm{BC}\), the Greek mathematician Archimedes is said to have discovered an important principle that is useful in density determinations. The story told is that King Hiero of Syracuse (in Sicily) asked Archimedes to verify that an ornate crown made for him by a goldsmith consisted of pure gold and not a gold-silver alloy. Archimedes had to do this, of course, without damaging the crown in any way. Describe how Archimedes did this, or if you don't know the rest of the story, rediscover Archimedes's principle and explain how it can be used to settle the question.

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)?
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