Question

49. A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder.
The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm
Find the capacity of the vessel.
100 2
con 2​

Answer 1

Given :

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder.The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm

$\:$

To find :

Find the capacity of the vessal.

$\:$

Solution :

Let the radius be R and height be H cm.

${ \red {\sf{Radius = \dfrac{14}{2} = 7cm}}}$

Height of the cylinder = 13 - 7 = 6cm

Total surface of Cylinder

$~$

2 (CSA of cylinder) + (CSA of Hemisphere)

$\: \:$

$: \implies \sf2(2\pi rh + 2\pi {r}^{2} )$

$\:$

$: \implies \sf4\pi r(h + r)$

$\:$

$: \implies\sf4 \times \dfrac{22}{7} \times 7 \times (6 + 7) {cm}^{2}$

$\:$

$\large{ \underline{ \boxed{ \color{blue} \sf1144 {cm}^{2} }}}$

Answer 2

${ \huge{ \underline {\pmb{ \bf{Given :}}}}}$

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder.The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm

$\:$

$\huge{ \underline{ \pmb{ \bf{To \: find : }}}}$

Find the capacity of the vessal.

$\:$

$\huge\underline{ \pmb{ \bf{Solution : }}}$

$~$

Let the radius be R and height be H cm.

$\pink \star \: { \red{ \color{blue}{ \sf{Radius = \dfrac{14}{2} = 7cm}}}}$

$\pink \star \: \color{blue} \sf {Height = 13 - 7 = 6cm }$

$~$

Total surface of Cylinder

$\: \:$

$\: \: \: : \implies \sf2(2\pi rh + 2\pi {r}^{2} )$

$\:$

$\: \: \: : \implies \sf4\pi r(h + r)$

$\:$

$\: \: \: : \implies\sf4 \times \dfrac{22}{7} \times 7 \times (6 + 7) {cm}^{2}$

$\:$

$\pink\star \: \large{ \underline{ \boxed{ \color{green} \bf1144 {cm}^{2} }}} \: \pink \star$