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Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 2r and height 2h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?

20 COINS Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 2r and height 2h. How many times greater is the surface area of Cyl class=

Answer :

The surface area of a cylinder is given by

[tex]A_A = 2\pi rh[/tex]

which is the surface area of cylinder A.

To compute the surface area of cylinder B, we have to map [tex](r,h)\mapsto (2r, 2h)[/tex] and we have the following formula

[tex]A_B = 2\pi(2r)(2h)[/tex]

If we manipulate the second expression, we have

[tex] A_B = 8\pi rh[/tex]

Which implies

[tex]\dfrac{A_B}{A_A} = \dfrac{8\pi rh}{2\pi rh} = 4 [/tex]

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