Prisma, Piramide, and Cilindro (Prism, Pyramid, and Cylinder)

This page continues with formulas for prisms, pyramids, and cylinders, expanding the formulario geometria solida pdf with more complex shapes.

Prisma (Prism)

The prism section provides formulas for volume (V), base area (Ab), lateral area (Al), and total area (At).

Definition: A prism is a 3D shape with two identical ends (bases) and flat sides.

• Volume (V) formula is provided (specific formula not given in the image) • Base Area (Ab) formula: Ab = V / h, where h is the height • Lateral Area (Al) formula: Al = Atot - 2Ab, where Atot is the total area • Total Area (At) formula: At = Alat + 2Ab, where Alat is the lateral area

Piramide (Pyramid)

The pyramid section includes formulas for volume (V), lateral area (Al), total area (At), and slant height $a$.

Definition: A pyramid is a 3D shape with a polygonal base and triangular faces meeting at a point (apex).

• Volume (V) formula: V = (Ab × h) / 3, where Ab is the base area and h is the height • Lateral Area (Al) formula: Al = (Ab × h) / 2 • Total Area (At) formula: At = Al + Ab • Slant height $a$ formula: a = √$r² + h²$, where r is the radius of the base

Cilindro (Cylinder)

The cylinder section provides formulas for volume (V), lateral area (Al), base area (Ab), and total area (At).

Definition: A cylinder is a 3D shape with two parallel circular bases connected by a curved surface.

• Volume (V) formula: V = πr²h, where r is the radius of the base and h is the height • Lateral Area (Al) formula: Al = 2πrh • Base Area (Ab) formula: Ab = πr² • Total Area (At) formula: At = Al + 2Ab = 2πr$r + h$

Highlight: These formulas are essential for students studying geometria solida terza media and preparing for exams.

Parallelepipedo and Cubo (Parallelepiped and Cube)

This page covers the formulas for parallelepipeds and cubes, two fundamental shapes in geometria solida.

Parallelepipedo (Parallelepiped)

The parallelepiped section provides formulas for lateral area (Al), total area (At), and volume (V).

Definition: A parallelepiped is a three-dimensional figure with six faces, each of which is a parallelogram.

• Lateral Area (Al) formula: Al = p × h, where p is the perimeter of the base and h is the height. • Total Area (At) formula: At = Al + (2 × Ab), where Ab is the area of the base. • Volume (V) formula: V = Ab × h

Highlight: Inverse formulas are provided, allowing calculation of perimeter, height, or base area when other values are known.

Cubo (Cube)

The cube section lists formulas for volume (V), base area (Ab), lateral area (Al), total area (At), and diagonal $d$.

Definition: A cube is a three-dimensional solid object with six square faces of equal size.

• Volume (V) formula: V = L³, where L is the length of a side. • Base Area (Ab) formula: Ab = L² • Lateral Area (Al) formula: Al = 4L² • Total Area (At) formula: At = Al + 2Ab • Diagonal $d$ formula: d = L√3

Example: For a cube with side length 5 cm, the volume would be 5³ = 125 cm³, and the diagonal would be 5√3 ≈ 8.66 cm.