Question

find the volume of a hollow hemispherical shell whose diameter of the internal and external surfaces are 10 cm and 14 cm respectively​

Answer 1

Step-by-step explanation:

$\sf \underline{ \underline{ \green{Given :}}} \\ \star \: \sf \: \mathfrak{Diameter \: of \: interna l \: surface} \\ \star \: \mathfrak{ Diameter \: of \: external \: surface}\\ \underline{ \underline{ \red{ \sf \: To \:Find} }} \\ \star \mathfrak{\: volume \: of \: a \: hollow \: hemispherical \: shell} \\ \underline{ \sf \underline{ \purple{Formula \: Used}}} \\ \sf \: Volume \: of \: the \: hemisphere \\ \leadsto \mathfrak{ \boxed{ \mathfrak{\frac{2}{3}\pi ( {R ^{3} - {r}^{3}}})} } \\ \sf \underline{ \underline{ \blue{Solution}}} \\ \tt \: External \: diameter = \mathfrak{14 \: cm} \\ \tt \: E xternal \: radius = \mathfrak{ \frac{14}{2} = 7cm} \\ \\ \tt Internal \: diameter = \mathfrak{ 5cm} \\ \tt Internal \: radius = \mathfrak{ \frac{10}{2} = 5cm} \\ \\ \bf \: Volume \: of \: the \: hollow \: hemispherical \\ \leadsto \: \mathfrak{ \frac{2}{3} \pi(R ^{3} - {r}^{3}) } \\ \leadsto \: \mathfrak{ \frac{2}{3} ( {7}^{3} - {5}^{3} ) } \\ \leadsto \: \mathfrak{ \frac{2}{3} \pi(343 - 125)} \\ \leadsto \: \mathfrak{ \frac{2}{3} \times \frac{22}{7} \times 218} \\ { \boxed{ \red{\mathfrak{ \frac{9592}{21 {cm}^{3}}}} }}$