The surface area of a cylinder can be calculated using the formula:
Surface area = 2πr² + 2πrh
where r is the radius of the base and h is the height of the cylinder.
Let's assume that the radius of the base of the smaller cylinder is r, then the radius of the base of the larger cylinder is 4/3 r, since the height is increased by 5 inches or 1/3 of the original height.
So, the surface area of the smaller cylinder is:
Surface area = 2πr² + 2πrh
And the surface area of the larger cylinder is:
Surface area = 2π(4/3 r)² + 2π(4/3 r)(15)
Simplifying these expressions, we get:
Surface area of smaller cylinder = 2πr² + 30πr
Surface area of larger cylinder = 2π(16/9 r²) + 40πr
Now we can find the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder:
Ratio = Surface area of larger cylinder / Surface area of smaller cylinder
= (2π(16/9 r²) + 40πr) / (2πr² + 30πr)
Simplifying this expression, we get:
Ratio = (32/9 r + 40) / (2r + 30)
= (32/9 r + 40) / 2(r + 15)
Since the cylinders are similar, the ratio of their surface areas is proportional to the square of the ratio of their heights:
Ratio = (20/15)²
= 1.7778
So the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder is approximately 1.7778, or 1.78 to two decimal places.