the interior of a building is in the form of a cylinder of diameter 4.2 m and height 3m surmounted by a cone of height equal to radius of the base. Find the surface area and volume of the interior of the building
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Answers
Step-by-step explanation:
Outer Surface area of the building = Curved surface area of cylindrical part + Curved surface area if the conical part. Curved Surface Area of a Cylinder of Radius "R" and height "h" =2πRh
Radius of the cylindrical part =
2
Diameter
=
2
4.2
=2.1m Curved surface area of a cone =πrl where r is the radius of the cone and l is the slant height.
Radius of the conical part =
2
Diameter
=
2
4.2
=2.1m
For a cone, l =
h
2
+r
2
where h is the height.
Hence, l =
2.1
2
+2.1
2
l=2.1
2
m
Hence, surface area of building =(2×
7
22
×2.1×4)+(
7
22
×2.1×2.1
2
)=72.4m
2
Volume of the building = Volume of the cylindrical part $ + VolumeofconicalpartVolumeofaCylinderofRadius"R"andheight"h" = \pi{ R }^{ 2 }h Volumeofacone = \frac { 1 }{ 3 } \pi { r }^{ 2 }h $$ where r
is the radius of the base of the cone and h is the height.
Hence, Volume of the pillar =(
7
22
×2.1×2.1×4)+(
3
1
×
7
22
×2.1
2
×2.1)=65.142m
3
Answer:
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