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A water tank, shown to the right, is shaped like an inverted cone with height 12 m and base radius 1.5 m. a. If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Use 1000 kg/m for the density of water and 9.8 m/s for the acceleration due to gravity. b. Is it true that it takes half as much work to pump all the water out of the tank when it is filled to half its depth as when it is full? Explain. a. Draw a y-axis in the vertical direction (parallel to gravity) and choose the bottom of the tank as the origin. For Osys 12, find the cross-sectional area Aly) in terms of y. Ay) =O (Simplify your answer. Type an exact answer, using z as needed. Use integers or fractions for any numbers in the expression.) Set up the integral that gives the work required to pump the water out of the tank. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Туре ехаct answers.) O A. O dy OB. The amount of work required is approximately (Type an integer or a simplified fraction. Type an exact answer, using x as needed.) b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Yes. It takes exactly half as much work to pump all the water out of the tank when it is half full. O B. No. The amount of work required to pump all the water out of the tank when it is half full is approximately J. (Type an integer or a simplified fraction. Type an exact answer, using x as needed.)

A water tank, shown to the right, is shaped like an inverted cone with height 12 m and base radius 1.5 m. a. If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Use 1000 kg/m for the density of water and 9.8 m/s for the acceleration due to gravity. b. Is it true that it takes half as much work to pump all the water out of the tank when it is filled to half its depth as when it is full? Explain. a. Draw a y-axis in the vertical direction (parallel to gravity) and choose the bottom of the tank as the origin. For Osys 12, find the cross-sectional area Aly) in terms of y. Ay) =O (Simplify your answer. Type an exact answer, using z as needed. Use integers or fractions for any numbers in the expression.) Set up the integral that gives the work required to pump the water out of the tank. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Туре ехаct answers.) O A. O dy OB. The amount of work required is approximately (Type an integer or a simplified fraction. Type an exact answer, using x as needed.) b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Yes. It takes exactly half as much work to pump all the water out of the tank when it is half full. O B. No. The amount of work required to pump all the water out of the tank when it is half full is approximately J. (Type an integer or a simplified fraction. Type an exact answer, using x as needed.)

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 43AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
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1.5 m A water tank, shown to the right, is shaped like an inverted cone with height 12 m and base radius 1.5 m. a. If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Use 1000 kg/m for the density of water and 9.8 m/s for the acceleration due to gravity. b. Is it true that it takes half as much work to pump all the water out of the tank when it is filled to half its depth as when it is full? Explain. 12 m a. Draw a y-axis in the vertical direction (parallel to gravity) and choose the bottom of the tank as the origin. For 0sys 12, find the cross-sectional area A(y) in terms of y. A(y) = D (Simplify your answer. Type an exact answer, using a as needed. Use integers or fractions for any numbers in the expression.) Set up the integral that gives the work required to pump the water out of the tank. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) O A. JO dy О в. dx The amount of work required is approximately (Type an integer or a simplified fraction. Type an exact answer, using n as needed.) b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Yes. It takes exactly half as much work to pump all the water out of the tank when it is half full. O B. No. The amount of work required to pump all the water out of the tank when it is half full is approximately J. (Type an integer or a simplified fraction. Type an exact answer, using a as needed.)
Transcribed Image Text:1.5 m A water tank, shown to the right, is shaped like an inverted cone with height 12 m and base radius 1.5 m. a. If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Use 1000 kg/m for the density of water and 9.8 m/s for the acceleration due to gravity. b. Is it true that it takes half as much work to pump all the water out of the tank when it is filled to half its depth as when it is full? Explain. 12 m a. Draw a y-axis in the vertical direction (parallel to gravity) and choose the bottom of the tank as the origin. For 0sys 12, find the cross-sectional area A(y) in terms of y. A(y) = D (Simplify your answer. Type an exact answer, using a as needed. Use integers or fractions for any numbers in the expression.) Set up the integral that gives the work required to pump the water out of the tank. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) O A. JO dy О в. dx The amount of work required is approximately (Type an integer or a simplified fraction. Type an exact answer, using n as needed.) b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Yes. It takes exactly half as much work to pump all the water out of the tank when it is half full. O B. No. The amount of work required to pump all the water out of the tank when it is half full is approximately J. (Type an integer or a simplified fraction. Type an exact answer, using a as needed.)
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