Question

A right triangle whose sides are 15cm and 20cm, is made to revolve about its hypotenuse. find the volume of the double cone. (π = 3.14)

Answer 1

heya friend .♠

Here is ur answer.....✌
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Let ∆ AOB be the given right triangle in which <AOB is rotated about the hypotenuse AB ,the two cones generated are AO'O And BOO'..

Clearly ,OA=15cm, OB=20cm.

in right -angled ∆ AOB, we have

AB=√15^2+20^2

AB=225+400

AB=√625

AB=25.

let OP =x cm
then
1/2*OA*OB=1/2*AB*OP

=>1/2*15*20=1/2*25*OP

=>150=25x

=>x=6cm

in right -angled ∆APO,we have

AP=√(OA)^2-(OP)^2

=√(15)^2-(6)^2

=√225-36

=√289

AP=17cm

BP=AB-AP=(25-17)=8cm

now ,•°•radius of each of the cones AO'O and BO'O,r =OP=6cm

Height of the cone AO'O ,H=AP=17cm

Height of the cone BOO' h=8cm.

volume of the double cone

=volume of the cone AO'O+bole of the cone BOO'H

=1/3πr^2h+1/3πr^2H

=1/3*3.14*(6)^2*8+ 1/3*(3.14*(6)^2*17

=>1/3*3.14(288+612)

=>1/3*3.14*900

=>942cm^3 Ans..

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hope it help you.

@Rajukumar☺☺