In a marriage ceremony of her daughter Poonam, Ashok has to make arrangements for the accommodation of 150 persons. For this purpose, he plans to build a conical tent in such a way that each person has 4 sq. meters of the space on ground and 20 cubic meters of air to breath. What should be the height of the conical tent ?<\/p>\n
Let the height of the conical tent = h metre.<\/p>\n
Radius of the base of the cone = r meter.<\/p>\n
The tent has to accommodate 150 persons.<\/p>\n
The space required by each person on the ground = 4 \\(m^2\\)<\/p>\n
And the amount of air = 20 \\(m^3\\)<\/p>\n
\\(\\therefore\\) Area of the base = 150 \\(\\times\\) 4 = 600 \\(m^2\\)<\/p>\n
\\(\\implies\\) \\(\\pi r^2\\) = 600 \\(\\implies\\) r = 13.817 m<\/p>\n
Volume of the air required for 150 persons = 150 \\(\\times\\) 20 = 3000 \\(m^3\\)<\/p>\n
\\(\\implies\\) \\(1\\over 3\\) \\(\\pi r^2 h\\) = 3000 \\(m^3\\)<\/p>\n
\\(\\implies\\) h = \\(3000 \\times 7 \\times 3\\over 22 \\times (13.817)^2\\) = 15 m<\/p>\n
Hence the height of the conical tent is 15 m.<\/p>\n","protected":false},"excerpt":{"rendered":"
Question : In a marriage ceremony of her daughter Poonam, Ashok has to make arrangements for the accommodation of 150 persons. For this purpose, he plans to build a conical tent in such a way that each person has 4 sq. meters of the space on ground and 20 cubic meters of air to breath. …<\/p>\n