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Question
The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the:
- radius of the floor,
- height of the tent,
- length of the canvas required to cover this conical tent if its width is 2 m.
Solution
i. Let r be the radius of the base of the conical tent, then area of the base floor = πr2m2
∴ πr2 = 154
`=> 22/7 xx r^2 = 154`
`=> r^2 = (154 xx 7)/22 = 49`
`=>` r = 7
Hence, radius of the base of the conical tent i.e. the floor = 7 m
ii. Let h be the height of the conical tent, then the volume
= `1/3pir^2hm^3`
∴ `1/3pir^2h = 1232`
`=> 1/3 xx 22/7 xx 7 xx 7 xx h = 1232`
`=> h = (1232 xx 3)/(22 xx 7) = 24`
Hence, radius of the base of the conical tent i.e. the floor = 7 m
iii. Let l be the slant height of the conical tent,
Then `= l = sqrt(h^2+r^2) m`
∴ `l = sqrt(h^2 + r^2)`
= `sqrt((24)^2 + (7)^2)`
= `sqrt(576 + 49)`
= `sqrt(625)`
= 25 m
The area of the canvas required to make the tent = `pirlm^2`
∴ `pirl = 22/7 xx 7 xx 25 m^2`
= 550 m2
Length of the canvas required to cover the conical tent of its width 2 m = `550/2` = 275 m
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