Question

in a cylinder the radius and height was quadrupled. How much bigger would the new surface area be then the original surface area.

Answer 1

we know that
if in a cylinder the radius and height was quadrupled
so
the scale factor is equal to 4
scale factor=4
and
new surface area=[scale factor]²*original surface area
new surface area=[4]²*original surface area
new surface area=16*surface area original

therefore
the new surface area will be 16 times the original surface area.

alternative method
we know that
surface area of cylinder=2*[area of the base]+perimeter of the base*height
area of the base=pi*r²
perimeter of the base=2*pi*r

original surface area=2*[pi*r²]+[2*pi*r]*h-----> 2*pi*r*[r+h]

if the radius and height was quadrupled
so
new surface area=2*pi*(4*r)*[4r+4h]-----> 2*pi*(4*r)*4*[r+h]
new surface area=16*[2*pi*r*(r+h)]----> 16*[original surface area]

the answer is
the new surface area will be 16 times the original surface area.

Answer 2

The original surface area is:
A = 2 * pi * r ^ 2 + 2 * pi * r * h
Where,
r: radio
h: height
The area when the dimensions are modified is:
A '= 2 * pi * (4r) ^ 2 + 2 * pi * (4r) * (4h)
Rewriting we have:
A '= 16 * 2 * pi * r ^ 2 + 16 * 2 * pi * r * h
A '= 16 (2 * pi * r ^ 2 + 2 * pi * r * h)
A '= 16A
Answer:
the new surface area would be 16 times bigger than the original surface area