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.

Answer 1

Given that:

Radius of the base ${\displaystyle r=\frac{d}{2}=\frac{20}{2}=10m}$

Height of the cylinder h₁ = 2.5 m

Height of the cone h₂ = 7.5 m

 

Slant height of the cone

${\displaystyle l=\sqrt{r^2+h^2}}$

${\displaystyle =\sqrt{{10}^2+{7.5}^2}}$

= 12.5 m

The total capacity of the tent is given by

${\displaystyle V=\pi r^2{h}_1+\frac{1}{3}\pi r^2{h}_2}$

${\displaystyle =r\times {10}^2\times 2.5+\frac{1}{3}\times \pi \times {10}^2\times 7.5}$

= π x 250 + π x 250

= 500π m³ 

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)

${\displaystyle =\frac{22}{7}\times 175}$

= 550 m²

Therefore, the total cost of the canvas is

= 100 x 550

= Rs. 55000

Hence, the total capacity and cost is V = 500π m³, and Rs. 55000