The cylinder and the cone have a common base, the top of the cone lies on the axis of the cylinder

The cylinder and the cone have a common base, the top of the cone lies on the axis of the cylinder, the height of the cone is 2: 5 at the height of the cylinder. find the volume of the cone if the volume of the cylinder is 375

In order to find the volume of the cone, we calculate the ratio of the volumes of the cone and the cylinder.

Cylinder volume formula:

V = Sb. H.

Cone volume formula:

V = 1/3 H.

From this we see that the volume of the cone is related to the volume of the cylinder as 1: 3. This means that if their heights were equal, then the volume of the cone would be equal to one third of the volume of the cylinder:

375/3 = 125 cm3.

But since their heights are related as 2: 5, then you need:

V · 2/5;

125 2/5 = 50 cm3.

Answer: the volume of the cone is 50 cm3.