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 π = $\frac{22}{7}$]
Answer & explanation
Correct answer: option 4
We know that,
Curved surface area of a cylinder = 2πRh
Curved surface area of a cone = πrl
We have,
Area of the canvas = 3861 m2
Diameter = 10.5 cm
then, radius of the base = 5.25 m
We also know that,
The curved surface area of each tent = Curved surface area of the cylindrical part + Curved surface area of the conical part
= 2π × 5.25 × 4 + π × 5.25 × 10
= π(42 + 52.5) = \(\frac{22}{7}\) × 94.5 = 297 m2
Now, the number of tents in the camp = \(\frac{3861}{297}\) = 13