An engineering apprentice is given a rectangular sheet of metal of dimensions 500mm x 300mm. She is asked to cut out four identical squares, one in each corner of the sheet, fold up the sides and weld the corner seams to make a metal box. What should she make the length of the sides of the squares in order to maximise the volume?
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An engineering apprentice is given a rectangular sheet of metal of dimensions 500mm x 300mm. She is asked to cut out four identical squares, one in each corner of the sheet, fold up the sides and weld the corner seams to make a metal box.
What should she make the length of the sides of the squares in order to maximise the volume?
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- In 1923, the United States Army (there was no United States Air Force at that time) set a record for in-flight refueling of airplanes. Using two refueling planes, an Airco DH-4B biplane was able to remain in flight for 39 h. During the flight, the refueling planes were able to air-transfer a total of 687 gallons of fuel to the plane in 9 refueling transfers. Assume that the refueling nozzle had a diameter of 1.55 in and each refueling took 2.35 min to perform. Calculate the velocity of the fuel through the nozzle. Assume that the fuel filled the entire cross-sectional area of the nozzle.Raw milk is stored at a dairy farm in a refrigerated cylindrical vat 6.50 feet wide and 12.5 feet high. If the vat contains 3.3 x 10² ft³ of milk, how many kg of milk does the vat contain, given that raw milk has a density of 1030 kg/m ? STARTING AMOUNT ADD FACTOR ANSWER RESET ( ) 1030 (0.001) 9.34 12 (2.54)3 0.01 (12) 0.1 1000 9600 10 0.001 (100) 0.083 (0.01) 103000 2.54 100 330 kg/m cm ft in ft in cm kgThe masses of a measuring cylinder before and after pouring some liquid into it are shown in the diagram. cm cm 200 200 100 100 liquid mass = 80 g mass = 180 g What is the density of the liquid? 120 9/cm B 100 g/cm 180 g/ cm 120 D 180 g/cm 140 B O D O A
- Your employer is planning to build several cylindrical storage tanks that will hold fuel. He has decided that all of the cylindrical storage tanks should be the same size, but due to space constraints, is unsure what the diameter and height of each tank should be. Also, he currently does not know exactly how much fuel he will need to store. You are tasked with creating a "flexible" spreadsheet for your employer that will calculate the total volume of several cylindrical storage tanks. The following requirements should be met: • The input section should include inputs for: tank diameter (feet), tank height (feet), number of tanks built and total amount of fuel to be stored (gallons). Enter the following values in the input section of your spreadsheet: O Tank Diameter (feet) = 28 o Tank Height (feet) = 20 o Number of Tanks Built (ea) = 3 O Total Amount of Fuel to be Stored (gal) = 275,000 • The calculation section should compute: o Volume of One Tank (cubic feet AND gallons) o Total…The masses of a measuring cylinder before and after pouring some liquid into it are shown in the diagram. cm3 cm3 200 200 100 100 liquid mass 80 g mass 180 g What is the density of the liquid? 100 g/cm3 100 g/cm3 140 A 180 g/cm3 120 180 D g/cm3 140 120 В D O A15 Tuesday 4/19 lapeuty of mi Students are given three cubes made of unidentified materials. They need to determine whether or not the three cubes are made of the same material. They measure the mass of each cube and record it in the table. A student immediately concludes that the cubes are made of three different materials. Cube Mass (g) A 42 C 7 What observation would best support the students' conclusion? A. The cubes all have the same volume. B. The cubes all have a shiny appearance. C. The cubes are all attracted to a magnet. D. The cubes all conduct heat.
- A cube 8.22 cm on each side is made of a metal alloy. After you drill a cylindrical hole 1.5 cm in diameter all the way through and perpendicular to one face, you find that the cube has a mass of 0.21 kg. What is the density of this metal? Use T = 3.14 Express your answers in kg m³ and in whole numbers (NOT SCIENTIFIC NOTATION).There is relatively little empty space between atoms in solids and liquids, so that the average density of an atom is about the same as matter on a macroscopic scale-approximately 103 kg/m³. The nucleus of an atom has a radius about 10-5 that of the atom and contains nearly all the mass of the entire atom. (a) What is the approximate density (in kg/m3) of nucleus? 1000000000000 x in kg/m3 (b) One remnant of a supernova, called a neutron star, can have the density of a nucleus. What would be the radius (in m) of a neutron star with a mass 1.3 times that of our Sun (the radius of the Sun is 7 x 108 m)? 7640 X mIt is known that a cubical object made of cast aluminum 0.213 m on a side contains a hollow cavity also in the shape of a cube but of unknown dimensions. If the mass of the object is 22.8 kg, determine the length of each side of the interior cubical cavity. The density of aluminum is 2.70 103 kg/m3.
- The wing span of an Airbus A300 is 44.8 m.a) What area is swept out per second when the plane is in level flight at 250 m s-1?Need Help: It is known that a cubical object made of cast aluminum 0.213 m on a side contains a hollow cavity also in the shape of a cube but of unknown dimensions. If the mass of the object is 22.8 kg, determine the length of each side of the interior cubical cavity. The density of aluminum is 2.70 103 kg/m3. Given Tip: How is the volume of the cubical object related to the volume of aluminum in the object and the volume of the cubical cavity? How is the mass of the cubical object related to the mass of aluminum in the object? Recall how the volume of a cube is related to the length of each side of the cube.In 1923, the United States Army (there was no United States Air Force at that time) set a record for in-flight refueling of airplanes. Using two refueling planes, an Airco DH-4B biplane was able to remain in flight for 39 h. During the flight, the refueling planes were able to air-transfer a total of 687 gallons of fuel to the plane in 9 refueling transfers. Assume that the refueling nozzle had a diameter of 1.45 in and each refueling took 2.45 min to perform. Calculate the velocity of the fuel through the nozzle. Assume that the fuel filled the entire cross-sectional area of the nozzle. velocity: m/s