Area of ​​Geometric Figures

When a sphere of radius is divided into four identical parts, find the total surface area of the quarter sphere.

A cone with a slant height of was turned around vertex as shown in the following figure, and returned to its initial position after turns. Find the surface area of this cone.

As shown in the following figure, part of the sphere of radius was cut off. What is the surface area of the cut?

After filling a cylinder of the radius of the circle at the base and the height of with water, the sphere was immersed in it and taken out, and the level of the water became , as shown in the following figure. Find the surface area of the sphere in this case.

What is the volume of a triangular pyramid cut from a rectangular parallelepiped to a plane passing through three vertices , , and ?

A wooden pipe with a diameter of is drilled into a cylindrical hole of diameter of . When the volume of this wooden pipe after the hole has been drilled is , what is the surface area?

Find the volume of the solid figure that results from cutting a cube with an edge of into a plane passing through four points , , , and , as shown in the following figure. (Here, the two points and are the mid-points of and , respectively.)

Find the surface area of the pyramid that is produced in this case.

Find the volume of the pyramid that is produced.

As shown in the following figure, a square hole with a side length of cut through the center of each side of a cube with a length of edge of . Find the surface area of this figure.

In the following figure, find the area of the shaded region.

In the following figure, points , , , and are the midpoints of each side of a square with a side length of . Find the area of the shaded region.

In the following figure, find the area of the shaded region when is a square with a side length of .