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
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Correct Answer: 275 m
Solution : Let the radius be $r$ and the height be $h$. Area of the base = 154 sq m ⇒ $\pi r^2$ = 154 $\therefore r$ = 7 m Volume of cone = $\frac{1}{3}\pi r^2 h$ ⇒ $1232 =\frac{1}{3}×\frac{22}{7}×7×7×h$ $\therefore h = 24$ m Slant height, $l$ = $\sqrt{h^2+r^2}$ = $\sqrt{24^2+7^2}$ = $\sqrt{625}= 25$ m $\therefore$ Area of the canvas $=\pi r l=\frac{22}{7}×7×25 = 550$ m2 Length of the canvas required to cover conical tent of width 2 m = $\frac{550}{2}$ = 275 m Hence, the correct answer is 275 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 : If the volume of a sphere is $179 \frac{2}{3}$ m3, what is its surface area?
Option 1: 221 m2
Option 2: 154 m2
Option 3: 144 m2
Option 4: 151 m2
Question : The volume of a solid cylinder is 2002 cm3 and its height is 13 cm. What is the area (in cm2) of its base? (Take $\pi=\frac{22}{7}$)
Option 1: 77
Option 2: 154
Option 3: 231
Option 4: 308
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
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