Let r represent the radius of cylinder.
We have been given that the height of a right circular cylinder is 1.5 times the radius of the base. So the height of the cylinder would be [tex]1.5r[/tex].
We will use lateral surface area of pyramid to solve our given problem.
[tex]LSA=2\pi r h[/tex], where,
LSA = Lateral surface area of pyramid,
r = Radius,
h = height.
Upon substituting our given values in above formula, we will get:
[tex]LSA=2\pi r\cdot (1.5)r[/tex]
Now we will find the total surface area of cylinder.
[tex]TSA=2\pi r(r+h)[/tex]
[tex]TSA=2\pi r(r+1.5r)[/tex]
[tex]TSA=2\pi r(2.5r)[/tex]
[tex]\frac{TSA}{LSA}=\frac{2\pi r(2.5r)}{2\pi r(1.5r)}[/tex]
[tex]\frac{TSA}{LSA}=\frac{2.5r}{1.5r}[/tex]
[tex]\frac{TSA}{LSA}=\frac{25}{15}[/tex]
[tex]\frac{TSA}{LSA}=\frac{5}{3}[/tex]
Therefore, the ratio of total surface area to lateral surface area is [tex]5:3[/tex].
