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
We know that if in<span> 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]</span>²*original surface area new surface area=[4]²*original surface area new surface area=16*surface area original
therefore <span>the new surface area will be 16 times the original surface area.
alternative method </span>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.
