Q. 124.0( 4 Votes )

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.

Answer :


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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