14. The interior of a building is in the form of a right
circular cylinder of diameter 4.2 m and height 4 m
surmounted by a cone. The vertical height of the
cone is 2.1 m. Find the outer surface area and volume
of the building.
Answers
Answer:
Step-by-step explanation:
we have
A is cone and B is cylinder
outer surface area of a building = c.s.a of cone + cs.a of eye
for cone
l= square root of 2.4 whole square + square root of 2.1 whole square
=
C.S.A=πrl+2πrh=πr(l+2h)
=22/7 x 21/10 x 111/10= 73.26 m square
Answer: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 $$ where r
is the radius of the base of the cone and h is the height.
Hence, Volume of the pillar =(
7
22
×2.1×2.1×4)+(
3
1
×
7
22
×2.1
2
×2.1)=65.142m
3
Step-by-step explanation:
Outer Surface area of the building = Curved surface area of cylindrical part + Curved surface area if the conical part. Curved Surface Area of a Cylinder of Radius "R" and height "h" =2πRh
Radius of the cylindrical part =
2
Diameter
=
2
4.2
=2.1m Curved surface area of a cone =πrl where r is the radius of the cone and l is the slant height.
Radius of the conical part =
2
Diameter
=
2
4.2
=2.1m
For a cone, l =
h
2
+r
2
where h is the height.
Hence, l =
2.1
2
+2.1
2
l=2.1
2
m
Hence, surface area of building =(2×
7
22
×2.1×4)+(
7
22
×2.1×2.1
2
)=72.4m
2
Volume of the building = Volume of the cylindrical part $ + VolumeofconicalpartVolumeofaCylinderofRadius"R"andheight"h" = \pi{ R }^{ 2 }h Volumeofacone = \frac { 1 }{ 3 } \pi { r }^{ 2 }h $$ 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