Exercise 42 Page 820

Let's consider two right cylinders C_1 and C_2. Below, we write the surface area of each cylinder.

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_2However, 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.

Next, let's find the lateral area of C_2.

As we can see, both cylinders have the same lateral area.

Finding the Surface Areas

Let's finding the surface area C_1.

Finally, let's find the surface area of C_2.

As we wanted, both cylinders have different surface areas.

Drawing the Cylinders

Below, we show the two cylinders with the dimensions used before.

Keep in mind that this is just an example, so your answer may vary.