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.

Answer 1

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 m³

The internal surface area of the solid is

`S=2pir^2+2pirh`

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

= 70.51 m²

Hence, the volume of the vessel and internal surface area of the solid is V = 56 m³, S= 70.51 m²