Question

A vessel in the form of hemisherical bowl mounted by a hollow cylinder . the diameter of the sphere is 14 cm . and the total height of the vessel is 13 cm . Find its capacity .

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Answer 1

Let r be the radius of the hemispherical bowl and h be the height of the cylinder.

Then, r=7cm and h=6cm

Total capacity of the bowl

= volume of the cylinder + volume of the hemisphere

=(πr

2

h+

3

2

πr

3

)cm

3

=πr

2

(h+

3

2

r)cm

3

=

7

22

×7

2

×(6+

3

2

×7)cm

3

=1642.66cm

3

Answer 2

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☃ ƛƝƧƜЄƦ ☃

$\small\red{{Radius \: of \: the \: hemispherical \: bowl \: , r = 7 cm \: . \: }} \\ \small \orange{{ The \: height \: of \: the \: cylinder \: , h = ( 13 - 7 ) cm = \: 6 cm}}$

$\small \pink{Now , \: total \: capacity \: of \: the \: bowl \: = \: volume \: of \: cylinder \: + \: volume \: of \: hemisphere}$

$= \small\red{{\pi \: r^{2}h + ( \frac{2}{3}\pi \: r^{3})cm^{3}}} \\ = \small\green{{\pi \: r^{2}(h + \frac{2}{3}r)cm^{2}}} \\ = \small \pink{{ \frac{22}{7} \times 7^{2} \times (6 + \frac{2}{3} \times 7)cm ^{3} }} \\ = \small\green{{22 \times 7 \times \frac{32}{3}cm^{3} = \frac{4928}{3}cm^{3}}} \\ = \small\red{{1642.66 \: cm^{3} }}$

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