Question

A vessel is in the form of hemispherical bowl mounted by a hollow cylinder. the diameter of the sphere is 14cm and the total height of the vessel is 13cm. find the capacity of the vessel .​

Answer 1

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$\sf \underline{Let ' \: understand \: the \: concept \: 1 'st}$

The question is from very intersting topic of mathematics. The topic is related to Surface area and volume Now let's see basic concept -

• Total capicity of the bowl = Volume of cylinder + Volume of hemisphere.

This question says that the diameter of the sphere is 14 cm. and the total height of vessel is 13 cm .Find the capicity of the vessel . And we know that how to find radius , height of cylinder and total capicity of the bowl.

Let's do it...!

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$\sf \underline {To \: find :- \: }$

$\sf \small{❒ \: Capicity \: of \: the \: bowl}$

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$\sf \underline{Solution :-}$

$\sf \small{Given \: that}$

$\small \sf{❒ \: Diameter = 14 \: cm \: } then \: the\: radius \: is : - \: \\ \\ \sf \small{❒ \: Radius = \frac{Diameter}{2} = \frac{ \cancel{14}}{ \cancel{2}} = 7 \: cm \: \: \: \: \: \: \: \: \: } \\ \\ \small\sf {❒ \: Height =13 - 7 = 6 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\sf \small{Now} \\ \\ \sf \small{Total \: capicity \: of \: the \: bowl \: = Volume \: of \: cylinder + Volume \: of \: hemisphere.</p><p>}$

$\sf \small \: {\implies ( \: \pi \: r^{2} h + \frac{2}{3}\pi \: r^{3} )} \: cm ^{3} \\ \\ \sf \small{ \implies\pi \: r ^{2}(h + \frac{2}{3} \: r) \: cm^{3} } \\ \\ \sf \small{ \implies \frac{22}{7} \times 7^{2} \times (6 + \frac{2}{3} \times 7 ) \: cm^{3} } \\ \\ \sf \small{ \implies \: 22 \times 7 \times \frac{32}{3} cm ^{3} = \frac{ \cancel{4928}}{ \cancel3} \: cm^{3} } \\ \\ \sf \small \red{ \implies \: 1642.66 \: cm^{3} .}$

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