A toy is in the form of a cone mounted on a hemisphere on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. find the total surface area of the toy.
Given: Height of toy = h = 31 cm
Radius of hemisphere = radius of base of cone = r = 7 cm
From the figure we can calculate height of cone as
Height of cone = hc = h - r
= 31 - 7 = 24 cm
∴ hc = 24 cm
Formula: surface area of hemisphere = surface area of sphere/2 = 2πr2
Curved surface area of cone = πrl
Where l is slant height
l = √(49 + 576) = 25 cm
∴ l = 25 cm
Total surface area of toy = curved surface area of cone + surface area of hemisphere
Surface area of hemisphere = 2 × π × r2
= 2 × (22/7) × 72
= 308 cm2
Curved surface area of cone = π × r × l
= (22/7) × 7 × 25
= 550 cm2
∴ Total surface area of toy = 308 + 550
= 858 cm2
∴ Total surface area of toy = 858 cm2