# A right triangle With sides 3cm,4cm and 5cm is revolved around its hypotenuse. Find volume of double cone thus generated.

2
by royaman949

## Answers

2015-02-17T20:29:03+05:30
Area of triangle ABC =
=
= 6cm^2
again ara of  triangle =

therefore BO =
= 12/5
area of both cones =
=
=
=
=
look at my doubts
2015-02-18T14:52:11+05:30
By using Pythagoras theorem.

AB² + AC² = BC²
9 + 16 = BC²
5 cm = BC

Now let OB be x cm
Then OC = BC - x = 5 - x cm

Now in triangle AOB.
OB² + OA² = AB²
OA² + x² = 9
OA² = 9 - x² --------------------------------------1

Similarly in triangle AOC
OA² + OC² = AC²
OA² = 16 - ( 5 - x )² ---------------------------2

From 1 and 2

9 - x²  = 16 - ( 5 - x )²
We will get
OB =  x = 9/5

And OC = ( 5 - 9/5 ) = 16/5

From 1 we will get ,
OA² = 9 - (9/5)²  = 144/25
OA = 12/5

Now ,

Volume of double cone = volume of smaller cone + volume of bigger cone
= 1/3 π (OA)² × OB + 1/3 π (OA)² × OC
= 1/3 π (OA)² × (OB + OC)
= 1/3 π (OA)² × (BC)
= 1/3 × 22/7 × (12/5)² × 5
= 1056/35
= 30.17 cm³