How Do We Use Right Triangles similarity?

In Figure 1 , right triangle ABC has altitude BD drawn to the hypotenuse AC. 

Figure 1 An altitude drawn to the hypotenuse of a right triangle.

The altitude drawn to the hypotenuse of a right triangle creates two similar right triangles, each similar to the original right triangle and similar to each other.

Figure 2 shows the three right triangles created in Figure 1 . They have been drawn in such a way that corresponding parts are easily recognized. 

Figure 2 Three similar right triangles from Figure 1 (not drawn to scale).

AB and BC are legs of the original right triangle; AC is the hypotenuse in the original right triangle; BD is the altitude drawn to the hypotenuse; AD is the segment on the hypotenuse touching leg AB and DC is the segment on the hypotenuse touching leg BC. Because the triangles are similar to one another, ratios of all pairs of corresponding sides are equal. This produces three proportions which are 

Here is a video to help you understand better how to solve these problems 

How Do We Calculate the Volume of a Sphere, cones, and pyramids ?

Spheres : A sphere is a perfectly round geometrical and circular object in three-dimensional space, such as the shape of a round ball.

To Find the Volume of a Sphere you have to use the formula

Cones: A solid or hollow object that tapers from a circular or roughly circular base to a point.

 To Find the Volume of a Cone you use the formula 

V=Bh/3

B is the area of the base

for a cone the base is a circle so the formula can also be written as V=r^2h/3

Pyramids:  a square or triangular base and sloping sides that meet in a point at the top

 To find the Volume of a Pyramid you use the same formula that you would use for a cone 

V=Bh/3

B is the area of the bases

the  base of this pyramid is a rectangle so you use length * width so you can also write the formula as V=LWH/3