Question : How many metres of 2-m-wide cloth will be required to make a conical tent with a diameter of the base of 14 m and a slant height of 9 m ignoring wastage?
Option 1: 66 m
Option 2: 88 m
Option 3: 99 m
Option 4: 77 m
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Correct Answer: 99 m
Solution : Let the length of the 2 m wide cloth be $a$ metre. Area of cloth = $2a$ m2 Diameter of tent = 14 m Radius of tent, $r$ = $\frac{14}{2}$ = 7 m Slant height, $l$ = 9 m The curved surface area of the cloth = $\pi rl$ = $\frac{22}{7} \times7\times9$ = 198 m2 Now, the Area of cloth = Curved surface area of the conical tent ⇒ $2a = 198$ $\therefore a = 99$ m Hence, the correct answer is 99 m.
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Question : A conical tent of height 10 m and base diameter 48 m was erected by a company in a park. Find the curved surface area of the tent (in m2).
Option 1: $576 \pi$
Option 2: $1248 \pi$
Option 3: $1152 \pi$
Option 4: $624 \pi$
Question : A conical tent has to accommodate 25 persons. Each person must have 4 m2 of space on the ground and 80 m3 of air to breathe. Find the height of the tent.
Option 1: 60 m
Option 2: 50 m
Option 3: 40 m
Option 4: 45 m
Question : The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is:
Option 1: 4 metres
Option 2: 7 metres
Option 3: 9 metres
Option 4: 6 metres
Question : The volume of a conical tent is 1232 m3 and the area of its base is 154 sq m. Find the length of the canvas required to build the tent, if the canvas is 2 m in width. (Take $\pi=\frac{22}{7}$)
Option 1: 270 m
Option 2: 272 m
Option 3: 276 m
Option 4: 275 m
Question : A conical tent with a radius of 6 units and a height of 8 units is to be made with canvas. How much canvas is needed to make the tent? (Rounded off to two places of decimals)
Option 1: 188.57 units
Option 2: 155.87 units
Option 3: 166.57 units
Option 4: 177.55 units
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