Answer :

Explanation: Here in order to find th outer surface area of building we need to simply add the curved surface areas of cone and cylinder.


Given height of cylinder = h = 4 m


Height of cone = h’ = 2.8 m


Diameter of cylinder = diameter of cone = d = 4.2 m


Radius of cone = Radius of cylinder = d/2 =4.2m/2 = 2.1 m


Outer surface area of building = C.S.A of cylinder + C.S.A of cone


Now, C.S.A of cylinder = 2πrh eqn1


Where r = radius of base of cylinder, h = height of cylinder


And C.S.A of cone = πrℓ eqn2


Where r = radius of base of cone, ℓ = Slant height of cone


We know in a cone


(Slant height)2 = (height)2 + (radius)2 (put the given values)


(ℓ)2 = (2.8)2 + (2.1)2


(ℓ)2 = 7.84 + 4.41


(ℓ)2 = 12.25


ℓ = √(12.25)


ℓ = 3.5 m


Now, C.S.A of cone = π × 2.1 × 3.5 (putting the values in eqn2)


C.S.A of cone = 7.35π m2eqn3


C.S.A of cylinder = 2 × π × 2.1 × 4 (putting the values in eqn1)


C.S.A of cylinder = 2 × π × 4.41 × 4


C.S.A of cylinder = 16.8π m2eqn4


Outer surface area of building = eqn3 + eqn4


Outer surface area = 7.35π + 16.8π


= 24.15π


Outer surface area =75.9 m2


The outer surface area of building is 75.9 m2.


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