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
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Correct Answer: 60 m
Solution : Given: 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. ⇒ The total base area = 4 × 25 = $\pi r^2$ = 100 m2 The volume of the cone = $\frac{1}{3}\pi r^2h$ where $r$ and $h$ are radius and height, respectively. The volume of the air required = 25 × 80 = 2000 m3. Let the cone's height be $h$ m. According to the question, $\frac{1}{3}\times 100\times h=2000$ ⇒ $h=\frac{2000\times 3}{100}=60$ m Hence, the correct answer is 60 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 : 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 has a radius of 7m and a vertical height of 24m. How many full bags of rice can be emptied in it if the space occupied by the rice in each bag is 2m3 ?
Option 1: 566
Option 2: 616
Option 3: 716
Option 4: 650
Question : The base of a pyramid is an equilateral triangle of side 10 m. If the height of the pyramid is $40 \sqrt{3}$ m, then the volume of the pyramid is:
Option 1: 1,000 m3
Option 2: 1,200 m3
Option 3: 9,00 m3
Option 4: 8,00 m3
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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