#### Question

A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. Find the capacity of the tent and the cost of the canvas at Rs 100 per square metre.

#### Solution

Given that:

Radius of the base `r=d/2=20/2=10 m`

Height of the cylinder h_{1} = 2.5 m

Height of the cone h_{2} = 7.5 m

Slant height of the cone

`l = sqrt(r^2+h^2)`

`=sqrt(10^2+7.5^2)`

= 12.5 m

The total capacity of the tent is given by

`V=pir^2h_1+1/3pir^2h_2`

`=rxx10^2xx2.5+1/3xxpixx10^2xx7.5`

= π x 250 + π x 250

= 500π m^{3}

The total area of canvas required for the tent is

S = 2πrh + πrl

= 2 x 3.14 x 10 x 2.5 + 3.14 x 10 x 12.5

= π(2 x 10 x 2.5 + 10 x 12.5)

= π(50 + 125)

`= 22/7xx175`

= 550 m^{2}

Therefore, the total cost of the canvas is

= 100 x 550

= Rs. 55000

Hence, the total capacity and cost is V = 500π m^{3}, and Rs. 55000