Question

A tent is in the form of a cylinder surmounted by a cone. The slant height of the cone is 10 m, and height of the cylinder is 8 m. If the diameter of the cylinder is 12 m, then find the total surface area of the tent.

• A. $390.2m^2$
• B. $290.2m^2$
• C. $490.2m^2$
• D. $690.2m^2$

Answer 1

The correct option is C $490.2m^2$

Given,
Slant height of the cone, l = 10 m
Height of the cylinder, h = 8 m
Diameter of the cylinder = 12 m
$\Rightarrow$ Radius of the cylinder, r = 6 m



Total surface area of the tent = Curved surface area of the cylinder + Curved surface area of the cone

Curved surface area of the cylinder $=2\pi rh$
$=2\times \frac{22}{7}\times 6\times 8=301.7m^2$

Curved surface area of the cone =$\pi rl$
$=\frac{22}{7}\times 6\times 10=188.5m^2$

$\therefore$ Total surface area of the tent $=301.7+188.5=490.2m^2$