# The interio

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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