Question

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Answer 1

Given,

Radius of the conical portion of the toy = 3.5 cm = r

Total height of the toy = 15.5 cm = H

If H is the length of the conical portion

Then,

Length of the cone (h) = H – r = 15.5 – 3.5 = 12 cm

Now, we know that

The curved surface area of the cone (S₁) = πrL, where L is the slant height of the cone.

L² = r² + h²

L² = 3.5² + 12²

L² = 12.25 + 144 = 156.25

L = 12.5

So,

S₁ = π (3.5)(12.5)

S₁ = 137.5 cm²

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

S₂ = 2π (3.5)²

S₂ = 77 cm²

Therefore,

The total surface area of the toy (S) = Curved surface area of the cone + curved surface area of the hemisphere

S = S₁ + S₂

S = 137.5 + 77

S = 214.5 cm²

Hence, the total surface area of the children’s toy is 214.5 cm² .