## Can two 3D shapes have the same volume?

If two 3D figures have the same height and the same cross-sectional area at every point along that height, they have the same volume.

### Can two different shapes have the same volume?

Yes. density is mass over volume. they have the same volume… so to have different densities they have to have different masses.

#### How two objects could have the same volume but different surface areas?

Answer: Yes. Take a cube of side 1, its volume is 1 and its surface is 6. Consider cutting the cube in 2 equal parts (of volume 1/2 and surface 4). Then if we multiply all sides by , the volume will be 1 and the surface will be , but note that the last value is not rational, while 6 is.

**Does Cavalieri’s principle say that two three-dimensional figures with the same volume have the same height and equal area at every cross section explain?**

Cavalieri’s principle tells us that if 2 figures have the same height and the same cross-sectional area at every point along that height, they have the same volume.

**How does volume and surface area relate to 2 dimensional area?**

There is no definite relation between area and volume, as area is two dimensional and volume is 3 dimensional.

## Can two objects with the same volume have different surface areas?

Surface area is a two-dimensional measure, while volume is a three-dimensional measure. Two figures can have the same volume but different surface areas. For example: A rectangular prism with side lengths of 1 cm, 2 cm, and 2 cm has a volume of 4 cu cm and a surface area of 16 sq cm.

### How is volume and surface area different?

Surface area is the sum of the areas of all the faces of the solid figure. Finding surface area of solid figure is like finding how much wrapping paper that is required to cover the solid; it is the area of the outside faces of a box. Volume is the amount of space inside of the solid figure.

#### What is Cavalieri’s principle How does Cavalieri’s principle compare to similarity of figures?

In plain English, Cavalieri stated “if two figures have the same height, and “matching” congruent widths everywhere along the height, the figures have the same area.” Note that the “congruent widths” need not be of the same lengths on each of the parallel lines.

**What does Cavalieri’s principle tell us?**

Cavalieri’s principle tells us that if 2 figures have the same height and the same cross-sectional area at every point along that height, they have the same volume. Created by Sal Khan.

Original Question: “Can two objects with the same volume have different surface areas?” Answer: Yes. Take a cube of side 1, its volume is 1 and its surface is 6. Consider cutting the cube in 2 equal parts (of volume 1/2 and surface 4).

**What are the two distinct measures used to define three-dimensional shapes?**

The two distinct measures used to define the three-dimensional shapes are volume and surface area. Generally, the three-dimensional shapes are obtained from the rotation of two-dimensional shapes. Thus, the surface area of any 2D shapes should be a 2D shape.

## What is the difference between total surface area and volume?

Total Surface Area (TSA) is the area of all the surfaces including the base of a 3D object Volume is defined as the total space occupied by the three-dimensional shape or solid object. The volume is denoted as “V”. It is measured in terms of cubic units. Three-dimensional shapes have many attributes, such as vertices, faces, and edges.

### What is the difference between 2D shapes and 3D shapes?

Whereas 2d shapes have only two dimensions,i.e. length and width. Examples of three-dimensional objects can be seen in our daily life such as cone-shaped ice cream, cubical box, a ball, etc. Students will come across these shapes in Class 6.