Question

a vessel is the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5. Find its capacity. (Give ans with steps​

Answer 1

EXPLANATION.

A vessels is the form of a hemisphere bowl

surmounted by a hollow cylinder.

The diameter of the hemisphere = 21 cm.

The total height of the vessels = 14.5

To find it's capacity.

According to the question,

Diameter of the hemisphere = 21 cm

Radius of the hemisphere = d/2 = 10.5 cm

$\rm \to \boxed{\green{\: volume \: of \: the \: hemisphere \: = \frac{2}{3} \pi {r}^{3} }}$

$\rm \to \: \frac{2}{3} \times \frac{22}{7} \times 10.5 \times 10.5 \times 10.5$

=> volume of hemisphere = 2425.5 cm³

=> Height of cylinder =

=> Total height of vessels - Radius of the

hemisphere.

=> 14.5 - 10.5 = 4 cm

$\rm \to \boxed{ \orange{\: volume \: of \: cylinder \: = \pi {r}^{2}h}}$

$\rm \to \frac{22}{7} \times 10.5 \times 10.5 \times 4 = 1386cm {}^{3}$

=> Total volume = volume of Hemisphere

part + volume of cylinder

=> 1386 + 2425.5 = 3811.5 cm³.

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is 3811.5 cm³

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$\huge\sf\blue{Given}$

✭ A vessel of the of a Hemisphere surmounted by a hollow cylinder

✭ The diameter of the hemisphere is 21 cm

✭ Total height of the vessel is 14.5 cm

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$\huge\sf\gray{To \:Find}$

◈ The Volume?

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$\huge\sf\purple{Steps}$

$\sf\underline{\underline{\sf Concept}}$

We shall first seperately find the volume of each of the figures and then add up their volume to get the net Volume of the vessel

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Volume of Hemisphere is given by,

$\underline{\boxed{\sf Volume_{Cylinder} = 2\pi r^3}}$

◕ Radius = $\sf\dfrac{21}{2} = \dfrac{21}{2} = 10.5 \ cm$

Substituting the given values,

➝ $\sf Volume = 2 \pi r^3$

➝ $\sf2 \times \dfrac{22}{7}\times 10.5^3$

➝ $\sf2\times \dfrac{22}{7} \times 1157.625$

➝ $\sf\green{Volume = 2425.5 \ cm^3}$

Similarly the volume of a hemisphere is given by,

$\underline{\boxed{\sf Volume_{Hemisphere} = \pi r^2h}}$

Substituting the given values,

➳ $\sf\pi \times 10.5^2 \times 4$

➳ $\sf\dfrac{22}{7} \times 110.25 \times 4$

➳ $\sf\red{Volume = 1386 \ cm^3}$

≫ Total Volume = Sum of the Volume of the two figures

»» Volume of Cylinder + Volume of Hemisphere

»» $\sf2425.5 + 1386$

»» $\sf\orange{Total \ Volume = 3811.5 \ cm^3}$

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