Question

A vessel is
in the form
of a hollow cylinder
mounted on hemispherfcal
bowl The diameter the
Sphere is l4CM and
the total height of
vessel is
13cm
find
the Capcicity of the vessel​

Answer 1

☯︎ Correct question:

• A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the hemispherical is 14 cm and the total height of the vessel is 13 cm. Find the capacity of the vessel

☯︎ Given Information:

• A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder.

• The diameter of the hemispherical is 14 cm.

• The total height of the vessel is 13 cm.

☯︎ Need To Find Out:

• The capacity of the vessel = ?

☯︎ Required Solution:

• Height of cylinder = Height of bowl - Radius of hemisphere

✪ Radius = Diameter/2

✪ Radius = 14/2

✪ Radius = 7 cm

So,

➪ Height of cylinder = 13 cm - 7 cm

➪ Height of cylinder = 6 cm

☯︎ Now:

• Capacity of bowl = Volume of hemisphere + Volume of cylinder

$\sf \: Capacity \: of \: bowl = \dfrac{2}{3} \pi \: r {}^{3} + \pi \: r {}^{2} h \\ \\ \sf \: Capacity \: of \: bowl = \dfrac{2}{3} \times \dfrac{22}{7} \times 7 {}^{3 } + \dfrac{22}{7} \times 7 {}^{2} \times 6$

$\sf \: Capacity \: of \: bowl = \dfrac{ \bigg(2 \times 22 \times 49 \bigg)}{3} + 22 \times 42$

$\sf \: Capacity \: of \: bowl = \dfrac{2156}{3} + 924 \\ \\ \sf \: Capacity \: of \: bowl =718.67 + 924 \\ \\ \sf \: Capacity \: of \: bowl = \underline{1642.67 \: cm {}^{3} }$

☯︎ Hence:

• The capacity of the vessel is 1642.67 cm³.

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Answer 2

Step-by-step explanation:

☯︎ Correct question:

• A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the hemispherical is 14 cm and the total height of the vessel is 13 cm. Find the capacity of the vessel

☯︎ Given Information:

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

☯︎ Need To Find Out:

• The capacity of the vessel = ?

☯︎ Required Solution:

• Height of cylinder = Height of bowl - Radius of hemisphere

✪ Radius = Diameter/2

✪ Radius = 14/2

✪ Radius = 7 cm

So,

➪ Height of cylinder = 13 cm - 7 cm

➪ Height of cylinder = 6 cm

☯︎ Now:

Capacity of bowl = Volume of hemisphere + Volume of cylinder

$Capacityofbowl= 32 πr 3 +πr 2 h</p><p>Capacityofbowl= 3 × 722 ×7 3 + 22 ×7 2×6</p><p> \begin{gathered} \sf \: Capacity \: of \: bowl = \dfrac{ \bigg(2 \times 22 \times 49 \bigg)}{3} + 22 \times 42\\\\\end{gathered} </p><p>Capacityofbowl= 3(2×22×49) +22×42</p><p> \begin{gathered}\sf \: Capacity \: of \: bowl = \dfrac{2156}{3} + 924 \\ \\ \sf \: Capacity \: of \: bowl =718.67 + 924 \\ \\ \sf \: Capacity \: of \: bowl = \underline{1642.67 \: cm {}^{3} } \\ \end{gathered}$

Capacity of bowl= 32156 +924

Capacityof bowl=718.67+924

Capacity of bowl= 1642.67cm³

The capacity of the vessel is 1642.67 cm³.