a vessel is in the form of hemispherical bowl mounted by a cone. The diameter of the hemisphere is 25cm,total height of vessel is 25cm. Find the capacity of vessel
Answers
Given data :
- A vessel is in the form of hemispherical bowl mounted by a cone.
- The diameter of the hemisphere is 25 cm and the total height of vessel is 25 cm.
To find : The capacity of vessel ?
Solution :
⟹ Diameter of hemisphere, d = 25 cm
⟹ Radius of hemidphere, r = d/2 = 25/2 = 12.5 cm
{A vessel is in the form of hemispherical bowl mounted by a cone.}
∴ Radius of hemidphere = Radius of cone
⟹ Radius of cone = 12.5 cm
⟹ Total height of vessel = 25 cm
Hence,
⟹ Height of cone
= Total height of vessel - Radius of hemisphere
⟹ Height of cone = 25 - 12.5
⟹ Height of cone = 12.5 cm
Now,
⟹ volume of cone
= ⅓ * π * r² * h
⟹ volume of cone
= ⅓ * 22/7 * (12.5)² * 12.5
⟹ volume of cone
= ⅓ * 22/7 * (12.5)² * 12.5
⟹ volume of cone
= ⅓ * 22/7 * 156.25 * 12.5
⟹ volume of cone
= ⅓ * 22/7 * 1953.125
⟹ volume of cone
= 22/21 * 1953.125
⟹ volume of cone
= 2046.130952 cm³
Now,
⟹ volume of hemisphere
= ⅔ * π * r³
⟹ volume of hemisphere
= ⅔ * 22/7 * (12.5)³
⟹ volume of hemisphere
= ⅔ * 22/7 * 1953.125
⟹ volume of hemisphere
= 44/21 * 1953.125
⟹ volume of hemisphere
= 4092.261905 cm³
Now,
⟹ volume of vessel
= volume of hemisphere + volume of cone
⟹ volume of vessel
= 4092.261905 + 2046.130952
⟹ volume of vessel
= 6138.392857 cm³
Answer : Hence, the capacity of the vessel is 6138.392857 cm³.
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