Question

A right angled triangle with sides 15 cm, 20 cm and 25cm is revolved about the side 15 cm. Name the solid so obtained and hence, find its volume. If it is revolved about the side 20cm, what would be the dimensions of the solid in that case?Also, find the ratio of the volume of the two solids obtained in both the cases.

Answer 1

Let ABC be the right triangle, right angled triangle at A, whose sides AB and AC measures 6 cm and 8 cm respectively.

∴ 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