The surface area \( A \) of a cylinder is calculated using the formula \( A = 2\pi r(h + r) \), where \( r \) is the radius and \( h \) is the height. If Jordyn triples both the radius and the height, the new radius and height would be \( 3r \) and \( 3h \), respectively. Plugging these values into the surface area formula gives \( A' = 2\pi (3r)(3h + 3r) = 2\pi (3r)(3(h + r)) = 18 \cdot 2\pi r(h + r) \), showing that the new surface area is 18 times the original surface area. Therefore, tripling both the radius and height increases the surface area by a factor of 18.
Solve the following mathematical problem involving the surface area of cylinders. Jordyn builds a cylinder with a given height and a given radius. She wonders what would happen to the surface area if she tripled both the radius and the height of the cylinder. In 3–5 sentences, explain what would happen to the surface area if she did both these things.(4 points)
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