A right triangle whose sides are 3cm and 4cm

Asked by admin @ 12/08/2021 in Math viewed by 303 People

A right triangle whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate.)

Answered by admin @ 12/08/2021

In the right angled triangle ABC (right angled at B)

AB= 4cm and BC= 3cm

AC= square root 3 square + 4 square = Square root 9+16 = Square root 25 = 5cm

Area of triangle ABC = ½ ABxBC = ½ ACxBO

ABxBC = ACxBO

4x3 = 5xBO

BO= 12/5 = 2.4cm

The volume of the required double cone = volume of the cone ABD + volume of the cone BCD

= 1/3 pi r square h1 + 1/3 pi r square h square

[where h1 and h2 are the heights of the cone ABD and BCD respectively]

Surface area of double cone = surface area of cone ABD + surface area of cone BCD

Pi r l1 + pi r l2

Pi r (l1 + l2)

22/7 x 2.4 x (4+3)

22/7 x 2.4 x 7

= 52.8 cm square

So the volume of double cone is 30.17 cubic cm and surface area of double cone is 52.8 sq cm

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