Question

A solid sphere is cut into four equal parts . Then , the total surface area of each part is _______ .

Answer 1

Given:

A solid sphere cut into 4 equal parts

To find:

The surface area of each part

Solution:

The surface area of each part is 2π$R^{2}$.

We can find the area by taking the following steps-

We know that when a sphere is cut into four equal parts, each part has two semi-circular faces and one curved surface.

Let us assume that the radius of the solid sphere is R.

Now, the total surface area of the sphere=4π$R^{2}$

Since the sphere is divided into four equal parts, the curved surface area of each part will be 1/4th of the total surface area of the sphere.

So, the curved surface area of each part of the sphere=1/4(4π$R^{2}$)

=π$R^{2}$

We know that each part has two semi-circular faces, each with the radius of the sphere.

The total surface area of each part of the sphere=Curved surface area of each part+ area of 2 semi-circular faces

=π$R^{2}$+2(1/2π$R^{2}$)

=π$R^{2}$+π$R^{2}$

=2π$R^{2}$

Therefore, the surface area of each part is 2π$R^{2}$.