Q. A right triangle ABC with sides 8 cm , 15 cm and 17cm is revolved about the side 15 cm.Find the volume of the solid so obtained.
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Verified answer
Answer:
∴ Hypotenuse BC=
(15)
2
+(20)
2
=
225
=25cm
AO(A'O) is the radius of the common base of the double cone fanned by revolving the triangle around BC.
Area of ΔABC=
2
1
×15×20=
2
1
BC×AO.
⇒150=
2
1
×25×AO
⇒AO=12cm
Volume of the double cone
=
3
1
π×AO
2
×BO+
3
1
π×AO
2
×CO
=
3
1
π×AO
2
(BO+CO)
=
3
1
π×AO
2
×BC
=
3
1
×3.14×12×12×25=3768cm
3
Surface area of the double cone
=π×AO×AB+π×AO×AC
=π×AO(AB+AC)
=3.14×12×(15+20)
=3.14×12×35=1318.8cm
2
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