A right triangle whose sides are 15 cm and 20 cm including the right angle is made to relove about its hypotenuse find the volume

1 thought on “A right triangle whose sides are 15 cm and 20 cm including the right angle is made to relove about its hypotenuse find the volume”

1. Step-by-step explanation:

   Let ABC be the right angled triangle such that AB=15cm and AC=20cm

   Using Pythagoras theorem we have

   ⇒BC

   2

   =AB

   2

   +AC

   2

   ⇒BC

   2

   =15

   2

   +20

   2

   ⇒BC

   2

   =225+400=625

   ⇒BC=25cm

   Let OB=x and OA=y

   Applying pythagoras theorem in triangles OAB and OAC we have

   AB

   2

   =OB

   2

   +OA

   2

   ;AC

   2

   =OA

   2

   +OC

   2

   ⇒15

   2

   =x

   2

   +y

   2

   ;20

   2

   =y

   2

   +(25−x)

   2

   ⇒x

   2

   +y

   2

   =225;(25−x)

   2

   +y

   2

   =400

   {(25−x)

   2

   +y

   2

   }−{x

   2

   +y

   2

   }=400−225

   ⇒(25−x)

   2

   −x

   2

   =175⇒x=9

   Putting x=9 in x

   2

   +y

   2

   =225 we get

   81+y

   2

   =225⇒y

   2

   =144⇒y=12

   Thus we have OA=12cm and OB=9cm

   Volume of the double cone = volume of cone CAA’ + volume of cone BAA’

   =

   3

   1

   π×(OA)

   2

   ×OC+

   3

   1

   π×(OA)

   2

   ×OB=

   3

   1

   π×12

   2

   ×16+

   3

   1

   π×12

   2

   ×9

   =

   3

   1

   ×3.14×144×253768cm

   3

   Surface area of the double cone = curved surface area of cone CAA

   ′

   + curved surface area of cone BAA

   ′

   =π×OA×AC+π×OA×AB

   =(π×12×20+π×12×15)cm

   =420πcm

   =420×π=420×3.14

   =1318.8cm

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