find the capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the figure is pi r square divided by 3 into 3 h - 2 r
Answers
Answer:
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Step-by-step explanation:
capacity of the following vessel will be:
πhr^2- 2/3πr^3 = (πr^2)/3 -(3h- 2r)
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The capacity of the cylindrical vessel with a hemisphere portion raised upward at the bottom is 1/3 * πr² [3h – 2r].
Step-by-step explanation:
It is given that,
A cylindrical vessel with a base in the shape of hemisphere raised upward at the bottom as shown in the figure attached below.
Let the radius of the cylindrical vessel be “r” units and the height of the vessel be “h” units.
Since from the figure, we can see that the hemisphere is raised from the inside at the bottom so the radius will be the same as the cylinder i.e., “r” units
In order to find the capacity of the vessel, we will first find the volume of the cylinder and then subtract the volume of the bottom raised hemispherical portion from it.
Therefore,
The volume of the cylinder = πr²h ….. (i)
And,
The volume of the hemisphere = (2/3) πr³ ….. (ii)
Thus, subtracting eq. (ii) from (i), we get
The capacity of the cylindrical vessel with a hemispherical portion raised upward at the bottom is given by,
= [πr²h] - [(2/3) πr³]
Taking common of similar terms
= πr² [h – (2/3)r]
= πr² [(3h – 2r)/3]
= (1/3) * πr² [3h – 2r]
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