Question

The volume of a conical tent is 1232 m³ and the area of the base floor is 154 m². Calculate the:

1. radius of the floor,
2. height of the tent,
3. length of the canvas required to cover this conical tent if its width is 2 m.

Answer 1

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