9.Water is draining out of the conical water cup shown below. The vertex ispomng down, the radius is 4 cm, and the height is 5 cm. Suppose the water is drainingout at the rate of 0.5 cm³cm deep? Make sure you include the units of your answer.How fast is the water depth y falling when the water is 2.5sec4 cm5 cm

Introduction: The rate of change function represents the rate at which one quantity changes in…

Answered: 9. Water is draining out of the conical…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter65: Achievement Review—section Six

Section: Chapter Questions

Problem 55AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...

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When the Radius Increases a. A rope is wrapped tightly around a wheel with radius of 2 feet. If the radius of the wheel is increased by 1 foot to a radius 3 feet, by how much must the rope be lengthened to fit around the wheel? b. Consider a rope wrapped around the Earths equator. We noted in Exercise 17 that the radius of the Earth is about 4000 miles. That is 21,120,000 feet. Suppose now that rope is to be suspended exactly 1 foot above the equator. By how much must the rope be lengthened to accomplish this? The Size of the Earth The radius of the Earth is approximately 4000 miles. a. How far is it around the equator? Hint: You are looking for the circumference of a circle b. What is the volume of the Earth? Hint: The volume of a sphere of radius r is given by 43r3. b. What is the surface area of the Earth? Hint: The surface area of a sphere of radius r is given by 4r2.
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.
Solve 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.
Tsunami 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?
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Compute the height of a prism with a base area of 2.7 square feet and a volume of 4.86 cubic feet.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid brass casting in the shape of a right circular cone has a base diameter of 4.36 inches and a height of 3.94 inches. Find the weight of the casting. Brass weighs 0.302 pound per cubic inch.
A piece in the shape of a pyramid with a regular octagon (eight sided) base is machined from a solid block of bronze. Each side of the octagon base is 9.36 inches long. The height of the piece is 7.08 inches. The octagon base area 4.829, where s is the length of a side of the octagon. a. Determine the volume of the piece. Round the answer to the nearest cubic inch. b. Determine the weight of the piece. Round the answer to the nearest pound. Note: One cubic foot of the bronze used weighs 547.9 pounds per cubic foot.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid right cylinder 9.55 centimeters high contains 1910 cubic centimeters of material. Compute the cross-sectional area of the cylinder.

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