#### Question

A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is `14/3` m and the diameter of hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.

#### Solution

Given that:

Radius of the same base `r=3.5/2=1.75 m`

Height of the cylinder `h=14/3m`

The volume of the vessel is given by

`V=pir^2h+2/3pir^3`

`=3.14xx1.75^2xx14/3+2/3xx3.14xx1.75^3`

= 56 m^{3}

The internal surface area of the solid is

`S=2pir^2+2pirh`

`=2xx3.14xx1.75^2+2xx3.14xx1.75xx14/3`

= 70.51 m^{2}

Hence, the volume of the vessel and internal surface area of the solid is V = 56 m^{3}, S= 70.51 m^{2}

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Solution for question: A Vessel is a Hollow Cylinder Fitted with a Hemispherical Bottom of the Same Base. the Depth of the Cylinder is `14/3` M and the Diameter of Hemisphere is 3.5 M. Calculate the Volume and the Internal Surface Area of the Solid. concept: Surface Areas and Volumes Examples and Solutions. For the course CBSE