Question

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per m².

Answer 1

Given,

Height of the tent = 77 dm

Height of a surmounted cone = 44 dm

Height of the Cylindrical Portion = Height of the tent – Height of the surmounted Cone

= 77 – 44

= 33 dm = 3.3 m

And, given diameter of the cylinder (d) = 36 m

So, its radius (r) of the cylinder = 36/2 = 18 m

Let’s consider L as the slant height of the cone.

Then, we know that

L² = r² + h²

L² = 18² + 3.3²

L² = 324 + 10.89

L² = 334.89

L = 18.3 m

Thus, slant height of the cone (L) = 18.3 m

Now, the Curved Surface area of the Cylinder (S₁) = 2πrh

S₁ = 2π (184.4) m² 

And, the Curved Surface area of the cone (S₂) = πrL

S₂ = π × 18 × 18.3 m² 

So, the total curved surface of the tent (S) = S₁ + S₂

S = S₁ + S₂

S = (2π18 × 4.4) + (π18 × 18.3)

S = 1533.08 m²

Hence, the total Curved Surface Area (S) = 1533.08 m²

Next,

The cost of 1 m² canvas = Rs 3.50

So, 1533.08 m² of canvas will cost = Rs (3.50 x 1533.08)

= Rs 5365.8