Question

A right triangle, whose base and height are 15cm and
20cm respectively is made to revolve about it's hypotenuse.Find the volume and surface area of the double cone so formed.
l hope many will answer
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Answer 1

ANSWER

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