A rectangular triangle with 3 and 4 cm legs rotates for the first time around the smaller leg

A rectangular triangle with 3 and 4 cm legs rotates for the first time around the smaller leg, and the second time around the larger leg. Compare the volumes of these cones.

At the very beginning, recall the formula for determining the volume of a cone:

V = (1/3) * п * R ^ 2 * h,

where R is the radius of the cone,
h is the height of the cone.

Then in the first case (when rotating around the smaller leg, i.e. R = 4 cm, h = 3 cm), the volume of the cone will be:

V = (1/3) * п * R ^ 2 * h = (1/3) * п * 4 ^ 2 * 3 = 16 * п.

In turn, in the second case (when rotating around the larger leg, i.e. R = 3 cm, h = 4 cm), the volume of the cone will be equal to:

V = (1/3) * п * 3 ^ 2 * 4 = 12 * п.

Answer: in the 1st case, the V cone is larger.