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 (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_forwardThe 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_forward
- a 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_forwardA coffee can is shaped like a cylinder with height 7 inches and radius 5 inches. Find (a) the surface area and (b) the volume of the can. Round to the nearest tenth.arrow_forward
- A vessel is in the shape of a right circular cone. This vessel contains liquid to a depth of 12.8 centimeters, as shown. How many liters of liquid must be added in order to fill the vessel? One liter contains 1000 cubic centimeters.arrow_forwardSolve these exercises. Find the cross-sectional area of metal in the triangular tubing shown. Round the answer to the nearest whole square millimeter.arrow_forwardSolve these exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Find the base diameter of a right circular cone that has a volume of 922.4 cubic centimeters and a height of 14.85 centimeters.arrow_forward
- Solve these exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A brass casting is in the shape of a right circular cone with a base diameter of 8.26 centimeters and a height of 18.36 centimeters. Find the volume. Round the answer to the nearest cubic centimeter.arrow_forwardThe radius length of the base of a right circular cylinder is 6 in. The height of the cylinder is 10 in. Find the exact a Lateral area b total area c volume.arrow_forwardSolve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. The frustum of a right circular cone has a larger base area of 40.0 square centimeters and a smaller base area of 19.0 square centimeters. The height is 22.0 centimeters. Find the volume. Round the answer to the nearest cubic centimeter.arrow_forward
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