A juice seller serves his customers using a glass as shown in figure .The inner diameter of the cylindrical glass is 7.5 cm but the bottom of the glass has a hemispherical portion raised ,which reduces the capacity of the glass .If the height of the glass is 20cm ,find the apparent capacity of the glass and its actual capacity.
[take pie=3.14]
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9th
Maths
Surface Areas and Volumes
Surface Area of Right Circular Cylinders and Cones
A juice seller was serving ...
MATHS
A juice seller was serving his customers using glass. The inner diameter of the cylindrical glass was 5 cm , but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of the glass was 10 cm, find what the apparent capacity of the glass was and what the actual capacity was (Use π=3.14)
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ANSWER
REF.Image.
Actual capacity of Glass= Volume of cylinder - Volume of hemisphere
⇒ volume of cylinder=πr
2
h
where r=
2
D
=
2
5
cm;
h=10cm;D=3.14
⇒3.14×(
2
5
)
2
×10
⇒3.14×6.25×10
⇒196.25cm
3
Volume of Hemisphere ⇒
3
2
πr
3
(r=
2
5
)
⇒
3
2
×3.14×(
2
5
)
3
⇒
3
2
×3.14×15.625
⇒32.7cm
3
∴ Actual capacity 196.25−32.7=163.55cm
3
and apparent capacity ⇒196.25cm
3
Answer:
Step-by-step explanation:
Actual capacity of Glass= Volume of cylinder - Volume of hemisphere
⇒ volume of cylinder=πr2h
where
r=2D=25cm;
h=10cm;D=3.14
⇒3.14×(25)2×10
⇒3.14×6.25×10
⇒196.25cm3
Volume of Hemisphere
⇒32πr3
(r=25)
⇒32×3.14×(25)3
⇒32×3.14×15.625
⇒32.7cm3
∴ Actual capacity 196.25−32.7=163.55cm3
and apparent capacity ⇒196.25cm3