Notice that the base areas are different. What must happen if you want the cylinders to have bases with different areas?
See solution.
Practice makes perfect
Let's consider two right cylinders C_1 and C_2. Below, we write the surface area of each cylinder.
Surface area of C_1
Surface area of C_2
S_1 = π r_1^2 + 2π r_1h_1
S_2 = π r_2^2 + 2π r_2h_2
We are told that the lateral areas are equal, and so, if we want the cylinders to have different surface areas, the radius of the bases must be different. That is, r_1≠ r_2.
r_1 ≠ r_2 ⇒ h_1≠ h_2
However, we must consider numbers so that r_1h_1 = r_2h_2. Below, we pick an example combination of numbers that works.
r_1 = 3, h_1 = 4 and
r_2 = 4, h_2 = 3
Finding the Lateral Areas
Let's find the lateral area of each cylinder, starting with C_1.
