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.)

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Solution

The double cone so formed by revolving this right-angled triangle ABC about its hypotenuse is shown in the figure.

Hypotenuse

= 5 cm

Area of ΔABC

Volume of double cone = Volume of cone 1 + Volume of cone 2

= 30.14 cm³

Surface area of double cone = Surface area of cone 1 + Surface area of cone 2

= πrl₁ + πrl₂

= 52.75 cm²

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