The curved surface of a solid metalic sphere is cut in such a way that the curved surface area of the new sphere is half of that previous one. Let us calculate the ratio of the volumes of the portion cut off and the remaining portion of the sphere.

Question

The curved surface of a solid metalic sphere is cut in such a way that the curved surface area of the new sphere is half of that previous one. Let us calculate the ratio of the volumes of the portion cut off and the remaining portion of the sphere.

Philoid · Accepted Answer

Curved surface area of initial sphere = 4πr²

Curved surface area of new sphere = (1/2) 4πr² = 2πr²

The other half’s surface area = 2πr²

So, both the parts are hemispheres, with equal curved surface area and same radius.

Curved Surface area of new sphere is half of the curved surface area of previous one. This implies that the sphere is cut into two equal parts and hence the volumes of the two parts after cutoff will be equal too. So, the ratio will be 1:1.