Question

A tent is in the shape of a right circular cylinder surmounted by cone. The total height and the diameter of the base are $13.5$ m and $28$ m, respectively. If the height of the cylindrical portion is $3$ m, find the total surface area of the tent.

Answer 1

Diameter $=28$ m
Radius $=\frac{28}{2}=14$ m ($=r$)
Height $h=3$ m
Curved Surface area of Cylinder $=2\pi rh$ square unit
$=2\times \frac{22}{7}\times 14\times 3$
$=264m^2$
Cone:
radius $=14$ m; $h=10.5$ m
Slant height $l=\sqrt{h^2+r^2}$
$=\sqrt{{\left(10.5\right)}^2+{14}^2}$
$=\sqrt{306.25}$
$=17.5$ m
Curved surface area of cone $=\pi rl$ square unit
$=\frac{22}{7}\times 14\times 17.5$
$=770m^2$
Total surface area of the tent $=264+770=1034m^2$.