# 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

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