Q.9 A right angled triangle of which the sides are 65, 60 and 25cm in length is made to turn
round its hypotenuse. Find the volume of the double cone thus formed.
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Answer:
The double cone so formed by revolving this right-angled triangle ABC about its hypotenuse is shown in the figure.
Hypotenuse, AC =
3
2
+4
2
=
9+16
=
25
=5 cm
Area of ΔABC=
2
1
×AB×AC
⇒
2
1
×AC×DB=
2
1
×4×3
⇒
2
1
×5×DB=6
So, DB =
5
12
=2.4 cm
The volume of double cone = Volume of cone 1 + Volume of cone 2
=
3
1
πr
2
h
1
+
3
1
πr
2
h
2
=
3
1
πr
2
[h
1
+h
2
]=
3
1
πr
2
[DA+DC]
=
3
1
×3.14×2.4
2
×5
=30.14 cm
3
The surface area of double cone = Surface area of cone 1 + Surface area of cone 2
=πrl
1
+πrl
2
=πr[4+3]=3.14×2.4×7
=52.75 cm
2
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