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 heights 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,

I² = r² + H²

I² = 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 = `22/7 xx 3.5 xx 6.95`

S₁ =  76.45 cm²

Curved surface area of cylinder (S₂) = 2πrh

S₂ = 2π(3.5)(10)

S₂ = `2 xx 22/7 xx 3.5 xx 10`

S₂  = 220 cm²

Curved surface area of hemisphere(S₃) = 2πr²

S₃ = `2 xx 22/7 xx 3.5^2`

S₃  = 77 cm²

Total surface area of the solid is given by

S = S₁ + S₂ +S₃

= 76.45 + 220 + 77

= 373.45 cm²