If the radius and the height of a right cylinder are both doubled, by what factor will the surface area increase?

Question

If the radius and the height of a right cylinder are both doubled, by what factor will the surface area increase?

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Natalia 2 weeks 2021-09-09T09:57:11+00:00 1 Answer 0

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    2021-09-09T09:58:35+00:00

    Answer:

    Doubling the radius and the height of a right cylinder will increase the value of its surface area by a factor of 4

    Step-by-step explanation:

    Mathematically, the surface area of a right cylinder can be calculated using the formula;

    A = 2 π r (r + h)

    now let’s double the radius and the height.

    Our new r becomes 2r and our new height becomes 2h. Substituting these into the area formula, we have

    A = 2 π (2r)( 2r+ 2h)

    Let’s factor out all the 2 , we have

    A = 4 π r (2(r+h))

    A = 8 π r( r + h)

    we can see that the value of the area has been increased by a factor of 4

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