Modern commercial airliners are largely made of aluminum, a...

Modern commercial airliners are largely made of aluminum, a light and strong metal. But the fact that aluminum is cheap enough that airplanes can be made out of it is a bit of historical luck. Before the discovery of the Hall-Héroult process in 1886, aluminum was as rare and expensive as gold. What would happen if airplanes had to be made of steel? The fuselage of the Boeing 777, which can carry 305 passengers, is approximately a hollow aluminum cylinder without ends, 64.0 m long, 6.2 m wide, and 2.5 mm thick (see sketch at right). The fuselage of an airplane Suppose this fuselage was made of steel (density 7.87 g/cm³) instead of aluminum (density 2.70 g/cm³), and let's say the average passenger has a mass of 83 kg. We'll also assume the engines can't lift any greater mass than they already do. Calculate the number of passengers that the Boeing 777 could carry if its fuselage was made of steel.

Transcript

00:01 Hello, in this question we need to find out the number of passengers lifted by steel plane.

00:08 So here, first of all, this aeroplane do use steel but they are not completely made out of the steel.

00:14 Steel is, steel it is sturdy and strong but also it is very heavy.

00:28 So the amount of lift needed to get a steel airplane off the ground makes it a bad choice for the main material often.

00:35 Aeroplane.

00:37 So most of the aeroplanes or airplanes they are made out of titanium, steel, aluminium and many other materials including composites.

00:49 Composites that can contain a variety of different material.

00:53 So here now for hollow aluminium cylinder here we have length is equal to 72 .0 meter width that is diameter here it is 8 .4 meter it is a thickness that is breadth here it is 2 .5 millimeter which can be converted into 2 .5 multiply by 10 x to the power minus 3 meter it is there so therefore here as the diameter it is given 8 .4 therefore r is equal to divide the half of this diameter that will be 8 .4 divided by 2 so this will become 4 .2 meter it is there now this is the inner radius.

01:43 Now outer radius we can represent it as by capital r that will be equal to 4 .2 meter plus 2 .5 multiply by 10 days to the power minus 3 meter that is the thickness so this will become 4 .2025 meter so this is the outer radius now volume of cylinder that will be equal to pi r square h from the outer radius minus pi r square h from the inner radius so here we have we can write it as that is pi h multiply by r square minus r square it is there so therefore here we have pi is equal to 3 .14 multiply by height it is 72 meter which is a length or the height of the height of the cylinder multiply by here this r square it is 4 .2025 square minus 4 .2 square it is there so therefore here on solving this we will have the value that is 4746 267 centimeter cube because from here we have 4 .746 meter cube it is there so therefore which can be converted into centimeter cube that is 1 meter cube here it is equal to 1 ,000 100 cube it is a 100 centimeter cube so now as we have the density it is equal to 2 .70 gram per centimeter cube so therefore here now we can calculate the mass we know that that is density is equal to mass divided by volume.

03:59 So from here we can find out this mass.

04:02 Mass is equal to density multiplied by volume.

04:05 So here density it is 2 .70 gram per centimeter cube multiply by here volume we have 4 -7 -4627 centimeter cube.

04:17 So therefore these units got cancelled out and here we will have the value 1 -2814 -920 .920 .9 .9...

Question

Please give Ace some feedback