Question

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

Answer 1

Hint: This question can easily be solved by using the concept of lateral surface area of both cone and cylinder as doing this and summing up those areas will give us the surface area of the tent. We will use the following formula.
Curved surface area of cone= $\pi rl$
Curved surface area of cylinder=$2\pi rh$

Complete step-by-step answer:
Given,
Height of cylindrical portion=3m
Total height =13.5m
Therefore, height of cone=13.5-3=10.5m
Diameter of cylindrical portion=28m
Radius of cylinder=$\dfrac{{28}}{2}$=14m
Radius of cylinder=Radius of cone
Total surface area of tent =curved surface area of cone +curved surface area of cylinder
Curved surface area of cone= $\pi rl$
Where ,$l = \sqrt {{r^2} + {h^2}} $
$
  l = \sqrt {{{(14)}^2} + {{(10.5)}^2}} \\
  l = \sqrt {306.25} \\
  l = 17.5m \\
$
Curved surface area of cone=$\pi rl$
$
   = \dfrac{{22}}{7} \times (14) \times (10.5) \\
   = 461.58{m^2} \\
$
Curved surface area of cylinder=$2\pi rh$
$
   \Rightarrow 2 \times \dfrac{{22}}{7} \times 14 \times 3 \\
   \Rightarrow 264 \\
$

Total surface area of tent =curved surface area of cone +curved surface area of cylinder
=461.58+264
= 725.58${m^2}$
Hence the answer to this question is 725.58 ${m^2}$.

Note: To solve such questions we need to recall the basic formulae of solid figure and need to know that the tent will cover only that part which we can look out so here we need not to find the area of the bases which are hidden this we need to keep in mind and then using the formula and putting the values will give you the right answer.