a cylinder has a surface area of 250cmsquared. the height is twice as big as the radius. what is the height of the cylinder? I already know the answer its 7.28cm I just have no idea how my teacher got that answer.. so if anyone knows how thatd be great :)
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Well you know the surface area is the area of the two bases plus the area of the rectangle created by the middle of the cylinder. So the area of the two bases is (pi)r^2 plus (pi)r^2 which is 2(pi)r^2. Then the area of the rectangle will be 2(pi)r times the height which is 2r which then equals 4(pi)r^2. Add those together and you get 6(pi)r^2. Set that equal to 250 and you should get the radius equal to about 3.64. Multiply that by 2 to get your height because the height was twice the radius. This gets you to 7.28 cm.
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Area of Cylinder = 2(pi)r(r+h) = 250
put r = 2h , 6(pi)r^2 = 250
r = 3.64
& h = 2r = 7.28
put r = 2h , 6(pi)r^2 = 250
r = 3.64
& h = 2r = 7.28