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

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