Q. 354.2( 18 Votes )

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 :


Explanation: The total surface area of the toy can be calculated by taking the sum of the Curved surface area of cone and that of hemisphere of same radius.


Given total height of toy = H = 15.5 cm


Radius of hemisphere = Radius of cone = r = 3.5 cm


Now the height of cone = h = total height – radius of hemisphere


Height of cone = h = 15.5 – 3.5


Height of cone = h = 12 cm


Let the slant height of the cone be ‘ℓ’ cm


Also we know that in a cone,


(Slant height)2 = (Height)2 + (Radius)2


2 = 122 + 3.52 (putting the values)


2 = 144 + 12.25


2 = 156.25


ℓ = √(156.25)


ℓ = 12.5 cm


C.S.A of cone = πrℓ


C.S.A of cone = π × 3.5 × 12.5 (putting the given values)


C.S.A of cone = 43.75π m2     eqn1


C.S.A of hemisphere = 2πr2


C.S.A of hemisphere = 2 × π × 3.52


= 2 × π × 12.25


= 24.5π m2      eqn2


Now total surface area of toy = eqn1 + eqn2


Total surface area of toy = 43.75π + 24.5π


= 68.25π


⇒The total surface area of toy (putting π= 22/7)


= 9.75 × 22


= 214.5 m2


The total surface area of the toy is 214.5 m2.

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