a solid consting of a cone standing on a hemisphere is imarsed in a cylinder of water as shown in fig find is left in the figure
Answers
Answer:
solid consisting of a right cone standing on a hemisphere is placed upright in a right circular cylinder full of water and touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60cm60cm and its height is 180cm180cm, the radius of the hemisphere is 60cm60cm and height of the cone is 120cm120cm, assuming that the hemisphere and the cone have common base.
Asked on December 26, 2019 byavatar
Shagun Kurapati
ANSWER
For the cylinder we have
Radius of the base=r=60cm=r=60cm
Height =h=180cm=h=180cm
Volume of water that the cylinder contains =V=\pi { r }^{ 2 }h=\left\{ \pi \times { 60 }^{ 2 }\times 180 \right\} {cm}^{3}=V=πr
2
h={π×60
2
×180}cm
3
For conical part, we have
Radius of the base =r=60cm=r=60cm
Height ={h}_{1}=120cm=h
1
=120cm
Volume of conical part {V}_{1}=\cfrac { 1 }{ 3 } \pi { r }^{ 2 }{ h }_{ 1 }=\cfrac { 1 }{ 3 } \pi \times { 60 }^{ 2 }\times 120{ cm }^{ 3 }=\left\{\pi \times { 60 }^{ 2 }\times 40 \right\} { cm }^{ 3 }V
1
=
3
1
πr
2
h
1
=
3
1
π×60
2
×120cm
3
={π ×60
2
×40}cm
3
For hemispherical part, we have
Radius =r=60cm=r=60cm
Volume of the hemisphere { V }_{ 2 }=\left\{ \cfrac { 2 }{ 3 } \pi \times { 60 }^{ 3 } \right\} { cm }^{ 3 }\quad V
2
={
3
2
π×60
3
}cm
3
\Rightarrow { V }_{ 2 }=\left\{ 2\pi \times { 60 }^{ 2 }\times 20 \right\} { cm }^{ 3 }=\left( 40\pi \times { 60 }^{ 2 } \right) { cm }^{ 3 }\quad \quad ⇒V
2
={2π×60
2
×20}cm
3
=(40π×60
2
)cm
3
Hence volume of the water left out in the cylinder
\Rightarrow V={ V }_{ 1 }-{ V }_{ 2 }\quad =\left\{ \pi \times { 60 }^{ 2 }\times 180-\pi \times { 60 }^{ 2 }\times 40-40\pi \times { 60 }^{ 2 } \right\} { cm }^{ 3 }=\pi \times { 60 }^{ 2 }\times \left\{ 180-40-40 \right\} { cm }^{ 3 }⇒V=V
1
−V
2
={π×60
2
×180−π×60
2
×40−40π×60
2
}cm
3
=π×60
2
×{180−40−40}cm
3
=\cfrac { 22 }{ 7 } \times 3600\times 100{ cm }^{ 3 }=
7
22
×3600×100cm
3
=\cfrac { 22\times 36 }{ 700 } { m }^{ 3 }=
700
22×36
m
3
=1.1314{ m }^{ 3 }=1.1314m
3
solution
Answered on December 26, 2019 by
avatar
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in the cone and calender for hemisphere I have top on the way