Question

A right triangle, whose side are 3 cm and 4 cm (other than hypotenuse) is made to revolve about is hypotenuse. Find the volume formed?

Answer 1

Given 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)=5 cm
Area of $\Delta ABC=\left(\frac{1}{2}\right)\times AB\times AC$
$\Rightarrow \left(\frac{1}{2}\right)\times AC\times OB=\left(\frac{1}{2}\right)\times 4\times 3$
$\Rightarrow \left(\frac{1}{2}\right)\times 5\times OB=6$
$\Rightarrow OB=\frac{12}{5}=2.4cm$
Volume of double cone=Volume of cone 1+ Volume of cone 2
$=\left(\frac{1}{3}\right)\pi r^2{h}_1+\left(\frac{1}{3}\right)\pi r^2{h}_2$
$=\left(\frac{1}{3}\right)\pi r^2(h_1+h_2)=\left(\frac{1}{3}\right)\pi r^2(OA+OC)=\left(\frac{1}{3}\right)\times 3.14\times (2.4{)}^2\times (5)=30.14c{m}^3$