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

Solution:

As per the parameters given in the question, we have

Diameter of the cylinder = 20 m

Radius of the cylinder = 10 m

Height of the cylinder (say h₁) = 2.5 m

Radius of the cone = Radius of the cylinder (say r) = 15 m

Height of the Cone (say h₂) =7.5 m

Let us consider L as the slant height of the Cone, then

L = $\sqrt{r^2+h_2^2}$

= $\sqrt{{15}^2+{7.5}^2}=12.5m$

Volume of the cylinder, $V_1=\pi r^2{h}_1=\pi (10{)}^2\times 2.5=250\pi m^3$

Volume of the Cone, $V_2=\frac{1}{3}\pi r^2{h}_2=\frac{1}{3}\times \frac{22}{7}\times (10{)}^2\times 7.5=250\pi m^3$

Therefore, The total capacity of the tent = volume of the cylinder + volume of the cone = V₁ + V₂

V = 250 π + 250 π

V = 500 π m³

Hence, the total capacity of the tent = V = 4478.5714 m³

The total area of the canvas required for the tent is S = 2 πrh₁ + πrL

S = 2(π)(10)(2.5) + π(10)(12.5)

S = 550 m²

Therefore, the total cost of the canvas is (100) (550) = Rs. 55000