The lower part of a tent is of shape of a right circular cylinder , the height of which is 3.5 metres . The upper part of the the tent is of a shape of a right circular cone . If the total height of the tent be 9.5 metre and it its diameter of base be 5 metre , then how much quantity of tarpailin will be required to make 14 such tents ?

Explanation

The diameter of the base of the tent = 5 cm
` :. ` the radius of the base of the tent = `5/2 ` m = 2.5 m
height of the cylindrical part = 3.5 m
` :.` the curve surface area of this ppart = ` 2pirh = 2 xx 22/7 xx 2.5 xx 3.5 ` sq - metre
= 55 sq- metre
The radius of the conical upper part of the tent = 2.5 m and height = `(9.5 - 3.5) m = 6 ` m
The slant height of the conical ` = sqrt(r^(2) + h^(2))`
or , ` l = sqrt((2.5)^(2) + (6)^(2)) `
or , `l = sqrt(42.25 )` m = 6.5 m
` :. ` the curved surface area of this conical part ` = pirl `
` = 22/7 xx 2.5 xx 6.5 ` sq- m
` :.` the tarpaulin required to make one tent = ` ( 55 + 22/7 xx 2.5 xx 6.5 ) `sq - metre
` :. ` the tarpaulin required to make 14 tent = ` 14 ( 55 + 22/7 xx 2.5 xx 6.5) ` sq - metre
Hence the required quantity of tarpaulin = 1485 sq - metre