A solid toy is in the form of a hemisphere a surmounted by a cone of height & radius of base are 7cm. This toy is
completely Immersed in a cylindrical vessel containing
full of water if the radius of base of the vessel is 7cm & its
height is 20cm Find the volume of water left in the vessel after immersion of the toy
And the roume a later left in the
is alto immersion in the hay Halle (3)
Answers
Given :- A solid toy is in the form of a hemisphere a surmounted by a cone of height & radius of base are 7cm. This toy is completely Immersed in a cylindrical vessel containing full of water if the radius of base of the vessel is 7cm & its height is 20cm .
To Find :- The volume of water left in the vessel after immersion of the toy ?
Answer :-
→ Volume of toy = Volume of hemisphere + Volume of cone
→ Volume of toy = (2/3)πr³ + (1/3)πr²h
since h = r,
→ Volume of toy = (2/3)πr³ + (1/3)πr³
→ Volume of toy = πr³(2/3 + 1/3)
→ Volume of toy = πr³(3/3) = πr³
→ Volume of toy = (22/7) * 7 * 7 * 7 = 22 * 49 = 1078 cm³ .
now,
→ Volume of cylinder = πr²h = (22/7) * 7 * 7 * 20 = 22 * 140 = 3080 cm³ .
then,
→ Volume of water left in the vessel after immersion of the toy = Volume of cylinder - Volume of toy { As toy will take out water equal to its volume.}
→ Required left volume = 3080 - 1078 = 2002 cm³ (Ans.)
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