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Chapter 1: Problem 60

A cylindrical glass bottle \(21.5 \mathrm{~cm}\) in length is tilled with cooking oil of density \(0.953 \mathrm{~g} / \mathrm{mL}\). If the mass of the oil needed to fill the bottle is \(1360 \mathrm{~g}\), calculate the inner diameter of the bottle.

Short Answer

Expert verified
The inner diameter of the bottle is approximately 7.226 cm.

Step by step solution

01

Express volume in terms of mass and density.

Since density = mass/volume, we can say volume = mass/density. Given, mass = 1360 g and density = 0.953 g/mL, we find volume by substituting the values which gives us volume = \(1360 \, \mathrm{g}/0.953\, \mathrm{g/mL} = 1427.49\, \mathrm{mL} \).
02

Use the Cylindrical Volume Formula.

To find the radius, we need to rearrange cylindrical volume formula \(V = πr^2h\), to \(r = \sqrt{V/πh}\). Given, \(V = 1427.49\, \mathrm{mL}\) and \(h = 21.5\, \mathrm{cm}\) (considering 1 cm = 10 mL), we get \(r = \sqrt{1427.49\, \mathrm{mL}/(π \times 21.5\, \mathrm{mL})}= 3.613\, \mathrm{cm}\).
03

Compute the Diameter of the Bottle.

The diameter of a circle is twice its radius. Therefore to find the diameter of the base of the bottle, we multiply the radius by 2, which gives us \(d = 2r = 2 \times 3.613\, \mathrm{cm} = 7.226\, \mathrm{cm}\).

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Most popular questions from this chapter

Chlorine is used to disinfect swimming pools. The accepted concentration for this purpose is 1 ppm chlorine, or \(1 \mathrm{~g}\) of chlorine per million grams of water. Calculate the volume of a chlorine solution (in milliliters) a homeowner should add to her swimming pool if the solution contains 6.0 percent chlorine by mass and there are \(2.0 \times 10^{4}\) gallons of water in the pool. ( 1 gallon \(=3.79 \mathrm{~L} ;\) density of liquids $=1.0 \mathrm{~g} / \mathrm{mL} .

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The following procedure was used to determine the volume of a flask. The flask was weighed dry and then filled with water. If the masses of the empty flask and filled flask were \(56.12 \mathrm{~g}\) and \(87.39 \mathrm{~g},\) respectively, and the density of water is \(0.9976 \mathrm{~g} / \mathrm{cm}^{3}\), calculate the volume of the flask in \(\mathrm{cm}^{3}\).

You are given a liquid. Briefly describe steps you would take to show whether it is a pure substance or a homogeneous mixture.

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