I posted the same question. In case, since I'm asking for more than one questjknstart from q2 and answer as many SETime (s)Volume (cm)00305.06010.29014.812019.915025.118030.2Questions:1. Analyze the data. Was the rate of change of volume with respect to timeconstant? Justify your answer and explain the results.2. Determine the initial volume of sand and write an equation for the volume of sandremaining in the cone after t seconds.3. Rearrange the formula V = r²h to solve or the depth. In order to get anequation for the depth as a function of volume, you must substitute for r in termsof h. This can be done using similar triangles as shown below.The ratio of the radius and the depth (height) is always constant regardless of thevolume of and in the cone. In the diagram, r represents the radius of the surfaceof the sand and h represents the depth. The variable R represents the radius ofthe cone and H represents the height of the cone.HVihRRh== ²:. r =Substitute the values for R and H and simplify to get an expression for r. Use this toreplace r in the equation for depth and simplify. This results in a formula for depth asa function of volume only.4. Substitute the volume in terms of time in your formula from step 2 to obtain anequation for the depth as a function of time.5. Determine the rate of change of depth with respect to time using your model fromstep 4.6. Determine the rate of change of depth with respect to time after 120 s using yourmodel from step 4.While sand was leaking out of the cone, data was recorded every 30 s tomeasure the depth of the sand inside the cone filter. These values are shown inthe table below.Time (s)Level of Sand (cm)06.0305.8605.6905.41205.14.81501804.47. Did the level of sand in the cone decrease at a constant rate? Justify youranswer and explain.8. Create a graph of the sand level versus time. Draw a line or curve of best fit anddetermine the rate at which the level of sand was changing after 120 s.9. Compare your answer from step 8 to the value obtained in step 6. Explain theresults.

Answered: Image /qna-images/answer/4c059c30-6f43-4d3a-97cb-0f689b1ff58c.jpg

Time (s) Volume (cm³) 0 0 30 5.0 60 10.2 90 14.8 120 19.9 150 25.1 180 30.2 Questions: 1. Analyze the data. Was the rate of change of volume with respect to time constant? Justify your answer and explain the results. 2. Determine the initial volume of sand and write an equation for the volume of sand remaining in the cone after t seconds. 3. Rearrange the formula V = r²h to solve or the depth. In order to get an equation for the depth as a function of volume, you must substitute for r in terms of h. This can be done using similar triangles as shown below. The ratio of the radius and the depth (height) is always constant regardless of the volume of and in the cone. In the diagram, r represents the radius of the surface of the sand and h represents the depth. The variable R represents the radius the cone and H represents the height of the cone.

Time (s) Volume (cm³) 0 0 30 5.0 60 10.2 90 14.8 120 19.9 150 25.1 180 30.2 Questions: 1. Analyze the data. Was the rate of change of volume with respect to time constant? Justify your answer and explain the results. 2. Determine the initial volume of sand and write an equation for the volume of sand remaining in the cone after t seconds. 3. Rearrange the formula V = r²h to solve or the depth. In order to get an equation for the depth as a function of volume, you must substitute for r in terms of h. This can be done using similar triangles as shown below. The ratio of the radius and the depth (height) is always constant regardless of the volume of and in the cone. In the diagram, r represents the radius of the surface of the sand and h represents the depth. The variable R represents the radius the cone and H represents the height of the cone.

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter61: Areas Of Circles, Sectors, And Segments

Section: Chapter Questions

Problem 24A: A piece shown by the shaded portion is to be cut from a square plate 128 millimeters on a side. a....

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