Question

The height of a right circular cylinder is 1.5 times the radius of the base. What is the ratio of the total surface area to the lateral (curved) surface area of the cylinder?

Answer 1

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 $1.5r$.

We will use lateral surface area of pyramid to solve our given problem.

$LSA=2\pi r h$, where,

LSA = Lateral surface area of pyramid,

r = Radius,

h = height.

Upon substituting our given values in above formula, we will get:

$LSA=2\pi r\cdot (1.5)r$  

Now we will find the total surface area of cylinder.

$TSA=2\pi r(r+h)$

$TSA=2\pi r(r+1.5r)$

$TSA=2\pi r(2.5r)$

$\frac{TSA}{LSA}=\frac{2\pi r(2.5r)}{2\pi r(1.5r)}$

$\frac{TSA}{LSA}=\frac{2.5r}{1.5r}$

$\frac{TSA}{LSA}=\frac{25}{15}$

$\frac{TSA}{LSA}=\frac{5}{3}$

Therefore, the ratio of total surface area to lateral surface area is $5:3$.