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
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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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Question : What will be the curved surface area of a cone of radius 5 cm and a slant height of 30 cm? (Use $\pi=3.14$)
Option 1: 234 m2
Option 2: 715 m2
Option 3: 543 m2
Option 4: 471 cm2
Question : The curved surface area of a cylinder, whose height is 10 cm, is 1320 cm2. What is the volume of this cylinder? [Use $\pi$ $\left.=\frac{22}{7}\right]$
Option 1: 1388 m3
Option 2: 0.001368 m3
Option 3: 0.1386 m3
Option 4: 0.01386 m3
Question : Find the curved surface area of a cone whose radius of the base is 7 cm and slant height is 8 cm. [Use $\pi=\frac{22}{7}$]
Option 1: 132 cm2
Option 2: 198 cm2
Option 3: 154 cm2
Option 4: 176 cm2
Question : The radius of a right circular cylinder is thrice of its height. If the height of the cylinder is 3.5 cm, what is the volume of the cylinder?
Option 1: 1124.25 cm3
Option 2: 1324.75 cm3
Option 3: 1468.25 cm3
Option 4: 1212.75 cm3
Question : A cone and a cylinder have the same height and the radius of the cone is twice of the radius of the cylinder: What is the ratio of the volume of the cone to that of the cylinder?
Option 1: 2 : 5
Option 2: 4 : 5
Option 3: 3 : 2
Option 4: 4 : 3
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