Question

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Answer 1

$\textsf{Radius = 7cm [Radius = ½ Diameter]}$

$\sf{\footnotesize{Height \: of \: the \: Cylinderical \: portion = 13 - 7 = 6cm}}$

Height of Cylinder = Total height- height(radius) of hemisphere

$\textsf{CSA of Cylinder = 2πrh}$

$\sf{CSA \: of \: Cylinder = 2 \times \frac{22}{ \cancel7} \times \cancel7 \times 6}$

$\sf \green{CSA \: of \: Cylinder = 264 {cm}^{2} }$

$\sf{CSA \: of \: Hemispherical \: Bowl =2π r^{2} }$

$\sf{CSA \: of \: Hemispherical \: Bowl =2 \times \frac{22}{ \cancel7} \times \cancel7 \times 7 }$

$\sf \green{CSA \: of \: Hemispherical \: Bowl = 308 {cm}^{2} }$

$\textsf{\footnotesize{ \fbox{\pink{TSA of the whole vessel = 308 + 264 = 572 cm²}}}}$