When you change the size of 3D shapes, it can really change how much space they take up, which we call volume. Let’s look at a few examples to understand this better:
Cubes: The volume of a cube is found using this simple formula: ( V = s^3 ). Here, ( s ) means the length of one side. If you double the side length, like going from 2 to 4, the volume changes a lot! It goes from ( 2^3 = 8 ) to ( 4^3 = 64 ). That’s a huge jump!
Prisms: For a rectangular prism, the volume is calculated using this formula: ( V = l \times w \times h ) (length times width times height). If you change one of these measurements, the volume will change too. If you make the height taller while keeping the base the same, the shape will become taller and have more space inside.
Cylinders: For cylinders, the volume is found with this formula: ( V = \pi r^2 h ). If you increase the radius (the distance from the center to the edge) or the height, the volume increases quickly, especially because of the ( r^2 ) part!
In conclusion, it’s really interesting how even small changes in size can make a big difference in volume.
When you change the size of 3D shapes, it can really change how much space they take up, which we call volume. Let’s look at a few examples to understand this better:
Cubes: The volume of a cube is found using this simple formula: ( V = s^3 ). Here, ( s ) means the length of one side. If you double the side length, like going from 2 to 4, the volume changes a lot! It goes from ( 2^3 = 8 ) to ( 4^3 = 64 ). That’s a huge jump!
Prisms: For a rectangular prism, the volume is calculated using this formula: ( V = l \times w \times h ) (length times width times height). If you change one of these measurements, the volume will change too. If you make the height taller while keeping the base the same, the shape will become taller and have more space inside.
Cylinders: For cylinders, the volume is found with this formula: ( V = \pi r^2 h ). If you increase the radius (the distance from the center to the edge) or the height, the volume increases quickly, especially because of the ( r^2 ) part!
In conclusion, it’s really interesting how even small changes in size can make a big difference in volume.