Question

In a right-angled triangle, whose sides are 3 cm and 4 cm (other than hypotenuse). Find the volume of the double cone so formed by revolving this right-angled triangle ABC about its hypotenuse.

Answer 1

Give that in a right angled triangle, whose sides are 3 cm and 4 cm (other than hypotenuse).
The double cone so formed by revolving this right-angled triangle ABC about its hypotenuse.
Hypotenuse $AC=O(32+42)=5cm$
Area of $\Delta ABC=\left(\frac{1}{2}\right)\times AB\times AC\Rightarrow \left(\frac{1}{2}\right)\times AC\times OB=\left(\frac{1}{2}\right)\times 4times3\Rightarrow \left(\frac{1}{2}\right)\times 5timesOB=6\Rightarrow OB=\frac{12}{5}=2.4cm.$
Volume of double cone = Volume of cone 1 + Volume of cone 2
$=\left(\frac{1}{3}\right)\pi r^2{h}_1+\left(\frac{1}{2}\right)\pi r^2{h}_2=\left(\frac{1}{3}\right)\pi r^2(h_1+h_2)=\left(\frac{1}{3}\right)\pi r^2(OA+OC)=\left(\frac{1}{3}\right)\times 3.14\times \left({2.4}^2\right)\times \left(5\right)=30.14c{m}^3$