The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8m, surmounted by a cone whose vertical angle is a right angle. Find the area of the surface and volume of the building.

Given that

r1 = Radius of the base of cylinder

r2 = Radius of the base of the cone = r1 = 2.15 m

 

h1 = 3.8 m

In Right angled ΔAOE, we have

In right angled ΔAOE

(OA)2 + (OE)2 = (AE)2

(2.15)2 + (OE)2 = (3.04)2

(OE)2 = (3.04)2 – (2.15)2

= 9.2416 – 4.6225

= 4.6191

∴ Height of cone, h2 = 2.15 m

l2 = (slant height) = 3.04 m

∴ Surface area of the building

= Surface area of cylinder + surface area of the cone

volume of building = (volume)Cylinder + (volume) cone

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