Question

A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the height of the cylindrical and conical portions are 10 cm and 6 cm, respectively. Find the total surface area of the solid. (Use π = 22/7).

Answer 1

Given,

Radius of the common base (r) = 3.5 cm

Height of the cylindrical part (h) = 10 cm

Height of the conical part (H) = 6 cm

Let, ‘l’ be the slant height of the cone

Then, we know that

l² = r² + H²

l² = 3.5² + 6² = 12.25 + 36 = 48.25

l = 6.95 cm

So, the curved surface area of the cone (S₁) = πrl

S₁ = π(3.5)(6.95)

S₁ = 76.38 cm² 

And, the curved surface area of the hemisphere (S₂) = 2πr²

S₂ = 2π(3.5)²

S₂ = 77 cm²

Next, the curved surface area of the cylinder (S₃) = 2πrh

S₂ = 2π(3.5) (10)

S₂ = 220 cm²

Thus, the total surface area (S) = S₁ + S₂ + S₃

S = 76. 38 + 77 + 220 = 373.38 cm²

Therefore, the total surface area of the solid is 373.38 cm².