Question

A student's adventure camp was organised for class X students for five days and their accommodation was planned in tents. Each tent is in the shape of a cylinder surrounded by a conical top. If the height and diameter of the cylindrical portion are 5.5 m and 30 m respectively and total height of the tent is 8.25 m. Find the length of the canvas used in making the tent, if the breadth of the canvas is 1.5 m.

Answer 1

this needs some patience in simplifying process.. figure plays a key role

Answer 2

Answer:

825 m

Step-by-step explanation:

A tent is in the shape of a cylinder surrounded by a conical top

Height of cylinder = 5.5 m

Diameter of cylinder = 30 m

Radius of cylinder = $\frac{30}{2}=15 m$

Total height of the tent is 8.25 m.

Height of cone = Total height - Height of cylinder

                         = 8.25 m - 5.5 m

                         = 2.75 m

Radius of cone = 15 m

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

Total Surface area of tent = $2\pi r h + \pi r \sqrt{h^2+r^2}$

                                            = $2\times \frac{22}{7} \times 15 \times 5.5 + \frac{22}{7} \times 15 \times \sqrt{2.75^2+15^2}$

                                            = $1237.5 m^2$

Now The Area of the cloth used is 1237.5 sq.m.

Breadth of the cloth = 1.5 m

So, Length = $\frac{Area}{Breadth}$

                  = $\frac{1237.5}{1.5}$

                  = $825 m$

Hence Length of the canvas used in making the tent, if the breadth of the canvas is 1.5 m.is 825 m