A tent has the shape of a cylinder with a conical top. Find the total surface area of the tent if the height and diameter of the cylindrical part are 2.1 m and 4 m, respectively, and the slant height of the top is 2.8 m.

According to the question, the required tent is,

The total surface area of the tent is the sum of the curved surface areas of each of the individual parts.

Diameter of the cylinder = 4 m

∴ Radius of the cylinder ($r$) = 2 m

Height of the cylinder ($h$) = 2.1 m

Slant height of the conical top ($l$) = 2.8 m

We know the curved surface area of the cylindrical portion $=2\pi rh$

$=2\mathrm{\pi }\times 2\times 2.1$

$=8.4\pi {\mathrm{m}}^2$

Curved surface area of the conical portion$=\pi rl$

$=\pi \times 2\times 2.8$

$=5.6\mathrm{\pi } {\mathrm{m}}^2$

Therefore, the total curved surface area of the tent $=8.4\pi +5.6\pi$

$=14\times \frac{22}{7}$

$=44 {\mathrm{m}}^2$