a semi circular thin sheet of metal of diameter 24cm is bent to form an open conical cup. find the capacity of the cup.
Answers
Answer:The is the diameter of 28 cm
Step-by-step explanation:
As we know that the circumference of a circle is given as-
Circumference =πr
Whereas, r is the radius of circle
Diameter of circular sheet =28cm
∴ Radius of circular sheet =
2
28
=14cm
Therefore,
Circumference of circular sheet =14π
When a semi-circular sheet is bent to form an open conical cup, the radius of the sheet becomes the slant height of the cup and the circumference of the sheet becomes the circumference of the base of the cone.
Slant height of cup (l)= Radius of circular sheet =14cm
Circumference of the base of cone = circumference of circular sheet =14π
Let r be the radius of the base of cone
∴2πr=14
⇒r=7cm
Let h be the height of cup.
Therefore,
l
2
=r
2
+h
2
(14)
2
=(7)
2
+h
2
⇒h=
196−49
=
147
=7
2
cm
Now,
Capacity of cup = Volume of cone
As we know that, volume of cone is given as-
V=
3
1
πr
2
h
Therefore,
Capacity of cup =
3
1
×
7
22
×(7)
2
×7
3
=622.4cm
3
Thus the capacity of the cup is 622.4cm
3
.
Hence the correct answer is 622.4cm
3
.