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Byju's Answer
Standard IX
Mathematics
Volume of a right circular cone
A semi circul...
Question
A semi circular sheet of metal of diameter
28
cm is bent into an open conical cup. Find the depth and capacity of cup.
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Solution
Diameter of the circular sheet is
28
cm
Radius
=
14
cm
Circumference of semicircular sheet
=
14
π
Now, the semicircular sheet is bent in to an open conical cup.
Slant height of conical cup
=
l
=
radius of circular sheet
=
14
cm
Circumference of the base of conical cup
=
Circumference of semicircular sheet
⇒
2
π
r
=
14
π
⇒
r
=
7
cm
Depth of conical cup
=
Height of cone
=
√
l
2
−
r
2
=
√
14
2
−
7
2
=
√
196
−
49
=
√
147
=
7
√
3
cm
Capacity of conical cup
=
Volume of cone
=
1
3
π
r
2
h
=
1
3
×
22
7
×
7
×
7
×
7
√
3
=
1078
√
3
3
c
m
3
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(
√
3
=
1.73
)
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