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 tent and the cost of the canvas at Rs 100 per square meter.

Answer 1

Given,

Diameter of the cylinder = 20 m

So, its radius of the cylinder (R) = 10 m

Height of the cylinder (h₁) = 2.5 m

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

Height of the Cone (h₂) = 7.5 m

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

L² = r² + h₂²

L² = 15² + 7.5²

L² = 225 + 56.25

L² = 281.25

L = 12.5 m

Now,

Volume of the cylinder = πR²h₁ = V₁

V₁ = π(10)² 2.5

V₁ = 250 πm³

Volume of the Cone = 1/3 × 22/7 × r² × h₂² = V₂

V₂ = 1/3 × 22/7 × 10² × 7.5

V₂ = 250π m³

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

V = 250 π + 250 π

V = 500π m³

Hence, the total capacity of the tent is 500π m³

And, the total area of 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 for canvas is (100) (550) = Rs. 55000