Question : In a camp, there are tents of the same shape and size. Each tent is cylindrical up to a height of 4 m and conical above it. The diameters of the bases of the cylinder and the cone are both 10.5 m and the slant height of the conical part is 10 m. If a total of 3861 m2 canvas is used in making all the tents, then how many tents are there in the camp? [ Use $\pi-\frac{22}{7}$ ]
Option 1: 11
Option 2: 7
Option 3: 19
Option 4: 13
Correct Answer: 13
Solution :
Given: Radius of the base = $\frac{10.5}{2}$ = 5.25 m
Height = 4 m
Slant height = 10 m
The curved surface area of each tent = curved surface area of the cylindrical part + curved surface area of the conical part
= $2\pi rh + \pi rl$
= $2\pi × 5.25 × 4 + \pi × 5.25 × 10$
= $\pi(42 + 52.5)$
= $\frac{22}{7} × 94.5$
= $297 \ m^2$
$\therefore$ The number of tents in the camp = $\frac{3861}{297} = 13$
Hence, the correct answer is 13.
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