A metal Sphere of radius Ym is melted down and remade into a cylinder of the same volume with height Ym with circular ends of radius 3m, find Y
The sphere has radius Y, so the volume of the sphere is 4/3 (pi) Y3 , The volume is the same for the cyclinder so we know the volume of the cylinder in terms of Y. Cyclinder volume = area of circle face x height. We know the circle has radius 3 so the area of the circle face is (pi) x 32 =9 x (pi). So we can find the volume of the cylinder in terms of Y; 9 x (pi) x Y = 9 x (pi) x Y As the volume of the sphere and cylinder are equal we can equate them (put them as equal to one another): 9 x (pi) x Y = 4/3 x (pi) x Y3 Dividing by (pi) on each side gives; 9 Y = 4/3 Y3 Subtract 9Y from both sides: 0 = 4/3 Y3 - 9Y Then Factorise: 0 = Y (4/3 Y2 -9) One solution to this is Y = 0, which makes sense mathematically but in the scenario given it doesnt make sense (as Y was the radius of the sphere. The other solution is found by saying that (4/3) x Y2 - 9 = 0 (as that is the other option for the above equation to be equal to 0) So solving that we can add 9 to both sides: 4/3 x Y2 = 9 Then multiplying by 3 4 Y2 = 27 Then dividing by 4 (you could have divided by 4/3 and done it in one step but you might find you need a calculator) Y2 = 27/4 OR 6.75
So Y = 2.60 (to 3sf) or leave as the square root of 27/4)
They might ask you to put it in a decimal form or in fraction, but they are both equal to one another.
