Question:
A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid.
Solution:
Volume of cylinder $=\pi r^{2} h$
$=\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 12$
$=462 \mathrm{~cm}^{3}$
Volume of 2 hemisphere $=4 \pi r^{3}$
$=\frac{4}{3} \times \frac{22}{2} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2}$
$=179.6 \mathrm{~cm}^{3}$
Therefore,
Volume of solid $=462+179.6$
$=641.6 \mathrm{~cm}^{3}$
Total surface area of the solid
$=2 \pi r h+4 \pi r^{2}$
$=2 \pi r(h+2 r)$
$=418 \mathrm{~cm}^{2}$