Concept explainers
Extended and Discovery Exercise
Exercises 1- 4: Measuring the thickness of a very thin layer of material can be difficult to do directly. For example. it would be difficult to measure the thickness of an oil film on water or a coat of paint with a ruler. However, it can be done indirectly using the following formula.
That is, the thickness of a thin layer equals the volume of the substance divided by the area that it covers. For example, if a volume of 1 cubic inch of paint is spread over an area of 100 square inches, then the thickness of the paint equals
- Thickness of an Oil Film A drop of oil measuring 0.12 cubic centimeter in volume is spilled onto a lake. The oil spreads out in a circular shape having a diameter of 23 centimeters. Approximate the thickness of the oil film.
- Thickness of Gold Foil A flat, rectangular sheet of gold foil measures 20 centimeters by 30 centimeters and has a mass of 23.16 grams. If 1 cubic centimeter of gold has a mass of 19.3 grams. find the thickness of the gold foil. (Source: U. Haber-Schaim. Introductory Apical Science.)
- Thickness of Cement A 100-foot-long sidewalk is 5 feet wide. If 125 cubic feet of cement are evenly poured to form the sidewalk, find the thickness of the sidewalk.
- Depth of a Lake A lake covers 2.5 X 107 square feet and contains 7.5 X 108 cubic feet of water. Find the average depth of the lake.
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College Algebra with Modeling & Visualization, Books a la Carte Edition plus MyLab Math with Pearson eText -- Access Card Package (6th Edition)
- The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of tin required for its construction. HINT: Include the lid and the base in the result.arrow_forwardSolve these exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Find the volume of a prism with a base area of 125 square inches and a height of 8 inches.arrow_forwardTsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height by reducing energy. See Figure 5.30. If a tsunami wave of height H in a channel of width W encounters a breakwater that narrows the channel to a width w, then the height h of the wave beyond the breakwater is given by h=HR0.5, where R is the width ratio R=w/W. a. Suppose a wave of height 8 feet in a channel of width 5000feet encounters a breakwater that narrows the channel to 3000feet. What is the height of the wave beyond the breakwater? b. If a channel width is cut in half by a breakwater, what is the effect on wave height? 16. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?arrow_forward
- The volume V of a cube is V=s3 , where s is the length of one side. Determine the volume of a cube with a side that measures 3.45 feet. Round your answer to 1 decimal place.arrow_forwarda For the through in the shape of half-cylinder, find the volume of water it will hold Use 3.14 and disregard the thickness b If the trough is to be painted inside and out, find the number of square feet to be painted Use 3.14.arrow_forwardSolve these exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Find the volume of a prism that is 13.82 centimeters high and has an equilateral triangle base that has 9.08 centimeter sides. Round the answer to the nearest cubic centimeter.arrow_forward
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