The total surface area of a solid right circular cylinder is 542 cm2. Its curved surface area is two-fifth of its total surface area. Find the curved surface area of the cylinder.

The correct answer is 216.8 cm².

Step 1: Understand the Given Information

We are given two pieces of information:
1. The total surface area (TSA) of a solid right circular cylinder is 542 cm².
2. The curved surface area (CSA) is two-fifth ($\frac{2}{5}$) of its total surface area.

Step 2: Express Curved Surface Area in terms of Total Surface Area

Using the given relationship, we can set up the equation:

$\text{Curved Surface Area (CSA)}=\frac{2}{5}\times \text{Total Surface Area (TSA)}$

Step 3: Calculate the Curved Surface Area

Substitute the given value of TSA = 542 cm² into the equation:

$\text{CSA}=\frac{2}{5}\times 542$

$\text{CSA}=\frac{1084}{5}$

$\text{CSA}=216.8{\text{cm}}^2$

Thus, the curved surface area of the cylinder is 216.8 cm².