A vessel is a hollow cylinder fitted with a hemispherical

Question:

A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is $\frac{14}{3} \mathrm{~m}$ and the diameter of hemisphere is $3.5 \mathrm{~m}$. Calculate the volume and the internal surface area of the solid.

Solution:

Given that:

Radius of the same base $r=\frac{3.5}{2}=1.75 \mathrm{~m}$

Height of the cylinder $h=\frac{14}{3} \mathrm{~m}$

The volume of the vessel is given by

$V=\pi r^{2} h+\frac{2}{3} \pi r^{3}$

$=3.14 \times 1.75^{2} \times \frac{14}{3}+\frac{2}{3} \times 3.14 \times 1.75^{3}$

$=56 \mathrm{~m}^{3}$

The internal surface area of the solid is

$S=2 \pi r^{2}+2 \pi r h$

$=2 \times 3.14 \times 1.75^{2}+2 \times 3.14 \times 1.75 \times \frac{14}{3}$

$=70.51 \mathrm{~m}^{2}$

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

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