A conical tent is 9m high and the radius of its base is 12m. (i) What is the cost of the canvas required to make it, if a square metre canvas costs Rs. 10? (ii) How many persons can be accommodated in the tent, if each person requires 2 square metre on the ground and 15 m^3 of space to breath in? (i) Given,
Height of tent`= 9 m`
Base radius`= 12 m`
Cost per `m^2= 10 per m^2`
Now,
Slant height`= sqrt[(9)^2+(12)^2]
`=sqrt[81+144]`
`=15`
Now,
Curved surface area`=pirl`
`=(22/7)xx12xx15`
`=3960/7`
`=565.7`
Now,
Total cost=`565.7xx10` `=₹5657`
(ii) area of ground `= pir^2`
`=452.16`
area required by each person is `2 m^2`
so
maximum no. of person `= 452.16/2`
`=226` persons
volume of conical tent `=(1/3)pir^2h`
`=(1/3)pi(12)^2(9)`
`=1356.48 m^3`
volume required by each person`=15 m^3`
maximum no of person `=1356.48/15`
`=90` persons

Explanation

(i) Given,
Height of tent`= 9 m`

Base radius`= 12 m`
Cost per `m^2= 10 per m^2`
Now,
Slant height`= sqrt[(9)^2+(12)^2]
`=sqrt[81+144]`
`=15`
Now,
Curved surface area`=pirl`
`=(22/7)xx12xx15`
`=3960/7`
`=565.7`
Now,
Total cost=`565.7xx10`
`=₹5657`
(ii) area of ground `= pir^2`
`=452.16`
area required by each person is `2 m^2`
so
maximum no. of person `= 452.16/2`
`=226` persons
volume of conical tent `=(1/3)pir^2h`
`=(1/3)pi(12)^2(9)`
`=1356.48 m^3`
volume required by each person`=15 m^3`
maximum no of person `=1356.48/15`
`=90` persons