Find the volume of a cone obtained by rotating an isosceles right-angled triangle with a hypotenuse of 3√2.

Let us denote by the variable n the value of the length of any leg of the triangle.

Since we know that the triangle is isosceles, and its hypotenuse is equal to 3√2 conventional units, we write down the equation and find what the length of the leg equals:

n ^ 2 + n ^ 2 = (3√2) ^ 2;

2n ^ 2 = 9 * 2;

n ^ 2 = 9;

n1 = 3;

n2 = -3.

Let’s calculate what the volume of the resulting cone will be, understanding that the radius in it is equal to the height:

V = 1/3 * 3.14 * 3² * 3 = 28.26.

Answer: The volume of the resulting cone = 28.26 cubic conventional units.