- 3d Figures and Volumes
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- Classifying Solids
- Vertices, Edges, and Faces of a Solid
- Volume of a Rectangular Prism
- Volume of a Rectangular Prism made of Unit Cubes
- Volume of a Solid made of Cubes with Unit Fraction Edge Lengths
- Volume of a Rectangular Prism with Fractional Edge Lengths
- Word Problem Involving the Volume of a Rectangular Prism
- Word Problem Involving the Rate of Filling or Emptying a Rectangular Prism
- Volume of a Triangular Prism
- Word Problem Involving the Volume of a Triangular Prism

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
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# Classifying Solids

Solid figures are classified into prisms, pyramids, cylinders, spheres and so on.

A **prism** is a solid that has two congruent bases which are parallel faces. The other faces of the prism are in the shape of rectangles. They are called lateral faces. A prism is named after the shape of its base.

The following diagrams show a triangular prism and a rectangular prism.

A **right prism** is a prism that has its bases perpendicular to its lateral surfaces.

A **Rectangular prism** is a prism that has rectangles as its bases. A shoe box, a soap box, a book, etc., are examples of rectangular prism.

A **Cube** is a special case of a rectangular prism where all faces and bases are congruent squares.

A dice, ice cubes, Rubik’s cube and so on are real world examples of cube shape.

A **triangular prism** is a prism that has triangles as its bases.

Prisms are named after the shape of their bases. A pentagonal prism has pentagons as its bases, a hexagonal prism has hexagons as its bases and so on.

## Cylinder

A **Cylinder** is a closed solid figure having two parallel circular bases connected by a rectangular curved face.

A **Sphere** is solid round figure where every point on its surface is equidistant from its centre.

A **Cone** is a closed solid figure whose circular base tapers into a point called apex.

## Pyramids

A pyramid is a solid figure that has a base, which can be any polygon, and three or more triangular faces that meet at a point called the apex. These triangular sides are called the lateral faces.

Use the diagram to identify the name of the following shape.

### Solution

**Step 1:**

The given figure is a prism whose bases are congruent rectangles.

**Step 2:**

The given figure is a rectangular prism.

Use the diagram to identify the name of the following shape.

### Solution

**Step 1:**

The given figure is a solid figure whose bases are congruent circles.

**Step 2:**

The given figure is a cylinder