
The picture shows the shape of a boiler. The total height of the boiler is and the diameter is 6 meters, the height of the cylindrical part is 6 meters too.
a. What is the height of the cone?
b. How many liters can the boiler hold? ( )

Answer
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Hint: To find the height of the cone, subtract the height of the cylinder and radius of the hemisphere from the total height of the boiler. To find how many liters the boiler can hold, add all the volumes, that is the volume of a cylinder, the volume of the hemisphere, and the volume of the cone.
So it is given in the question that the total height of the boiler
So the diameter of the cylindrical part .
Also the diameter of the hemispherical part .
So, we can say that, Diameter of cylindrical part Diameter of the hemispherical part .
Also the height of the cylindrical part .
So it is mentioned in the question that we have to find the height of the cone and how many liters the boiler can hold.
So now, first, we have to find the height of the cone.
For the height of the cone, we can see in the diagram that for calculating the height of the cone we need to subtract the height of the cylinder and radius of the hemisphere from the total height of the boiler.
So Height of cone Total height of boiler height of cylinder radius of the hemisphere
So we have a height of cylinder , and radius of the hemisphere which is half of the diameter i.e. .
So Height of cone .
Hence, we get the height of the cone as .
So now we have to find how many liters the boiler can hold.
So to find how many liters the boiler can hold, we have to find the volume of the boiler.
So for that, we have to consider all the volumes, i.e. volume of a cylinder, the volume of the hemisphere, and volume of a cone.
So the volume of a cylinder .
The volume of the hemisphere .
The volume of a cone .
where the radius of cylinder= radius of hemisphere= radius of cone and height of the cylinder.
So Volume of boiler volume of cylinder volume of hemisphere volume of a cone.
So we know all the values are mentioned above. Hence, substituting the values we get that,
the volume of the boiler .
The volume of the boiler .
.
..
.
It is given that litre.
So the volume of the boiler litre.
So we get the height of the cone as and volume of the boiler as litre.
Note: Read the question carefully and solve it accordingly. You should know the volume of a cylinder, the volume of the hemisphere, and also the volume of the cone. So don’t confuse yourself while solving or substituting the values.
Don’t make mistakes while writing the radius or don’t mix up the radius and height of each other. Give a proper name for height and radius.
So it is given in the question that the total height of the boiler

So the diameter of the cylindrical part
Also the diameter of the hemispherical part
So, we can say that, Diameter of cylindrical part
Also the height of the cylindrical part
So it is mentioned in the question that we have to find the height of the cone and how many liters the boiler can hold.
So now, first, we have to find the height of the cone.
For the height of the cone, we can see in the diagram that for calculating the height of the cone we need to subtract the height of the cylinder and radius of the hemisphere from the total height of the boiler.
So Height of cone
So we have a height of cylinder
So Height of cone
Hence, we get the height of the cone as
So now we have to find how many liters the boiler can hold.
So to find how many liters the boiler can hold, we have to find the volume of the boiler.
So for that, we have to consider all the volumes, i.e. volume of a cylinder, the volume of the hemisphere, and volume of a cone.
So the volume of a cylinder
The volume of the hemisphere
The volume of a cone
where
So Volume of boiler
So we know all the values are mentioned above. Hence, substituting the values we get that,
the volume of the boiler
The volume of the boiler
It is given that
So the volume of the boiler
So we get the height of the cone as
Note: Read the question carefully and solve it accordingly. You should know the volume of a cylinder, the volume of the hemisphere, and also the volume of the cone. So don’t confuse yourself while solving or substituting the values.
Don’t make mistakes while writing the radius or don’t mix up the radius and height of each other. Give a proper name for height and radius.
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