A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

Problem Restatement

Rotating a right triangle about one leg forms a right circular cone: the axis (height) is the leg of rotation and the radius is the other leg.

Given data

• Right triangle sides: 3 cm, 4 cm, 5 cm (hypotenuse = 5 cm)
• Rotation about the side of 3 cm

Concept / Approach

Here, height h = 3 cm (axis of rotation) and radius r = 4 cm (the other perpendicular leg). The slant height (5 cm) is not needed for volume.

Step-by-step calculation

Cone volume V = (1/3)πr^2h= (1/3)π(4^2)(3) = (1/3)π × 16 × 3 = 16π cm^3

Final Answer

Volume of the cone = 16π cm^3.