Find the volume of the body obtained by rotating a rectangular triangle with a leg of 6 cm

Find the volume of the body obtained by rotating a rectangular triangle with a leg of 6 cm and a hypotenuse of 10 cm around the large leg.

Rotating the triangle forms a cone, the radius of which r is the smaller leg, and the height h is the larger leg of the triangle. Let us denote the hypotenuse with and define h.

h ^ 2 = c ^ 2 – r ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64

r = 8 cm.

The volume of the cone is V = 1/3 * n * r ^ 2 * h = 1/3 * 3.14 * 6 ^ 2 * 8 = 301.4 cm3.

Answer: The volume of the cone is 301.4 cm3.