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

We can create the figure of the toy as per the given information

From the figure, it’s clear that the total surface area of the toy includes the curved surface area (CSA) of the cone and  hemisphere

Total surface area of the toy = CSA of the hemisphere + CSA of the cone

We will find the total area of the toy by using formulae;

CSA of hemisphere= 2πr², where 'r' is the radius of the hemisphere

CSA of cone = πrl, where 'r' and 'l' are the radius and slant height of the cone respectively.

Radius of the hemisphere, r = 3.5 cm

Height of the hemisphere = radius of the hemisphere, r = 3.5 cm

Radius of the cone, r = 3.5 cm

Height of the cone = Total height of the toy - height of the hemisphere

h = 15.5 cm - 3.5 cm = 12 cm

Slant height of the cone, l = √(r² + h²)

l = √[(3.5 cm)² + (12 cm)²]

l = √[12.25 cm² + 144 cm²]

l = √ 56.25 cm²

l = 12.5 cm

Total surface area of the toy = CSA of the hemisphere + CSA of the cone

= 2πr² + πrl

= πr (2r + l)

= 22/7 × 3.5 cm × (2 × 3.5 cm + 12.5 cm)

= 22/7 × 3.5 cm × (7 cm + 12.5 cm)

= 11 cm × 19.5 cm

= 214.5 cm²

Thus, the total surface area of the toy is 214.5 cm².