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