Scale Factor and Changing Dimensions

Front

What is a scale factor in relation to dimensions of a geometric shape?

Back

A scale factor is a number that scales, or multiplies, the dimensions of a geometric shape. It determines how much larger or smaller the new dimensions will be compared to the original dimensions.

Front

How does changing one dimension of a rectangular prism affect its volume?

Back

If one dimension (length, width, or height) of a rectangular prism changes, the volume changes by the same scale factor as that dimension.

Front

What is the formula for calculating the volume of a rectangular prism?

Back

The volume of a rectangular prism is calculated using the formula: Volume = length × width × height.

Front

If the width of a rectangular prism is doubled, how does that affect the volume?

Back

If the width is doubled, the volume also doubles, assuming the other dimensions remain constant.

Front

What happens to the volume of a rectangular prism if all dimensions are multiplied by a scale factor of 3?

Back

If all dimensions are multiplied by a scale factor of 3, the volume increases by a factor of 3^3 (27), meaning the new volume is 27 times the original volume.

Front

If the height of a rectangular prism is halved, what happens to the volume?

Back

If the height is halved, the volume is also halved, assuming the other dimensions remain constant.

Front

What is the relationship between the dimensions of a rectangular prism and its volume?

Back

The volume of a rectangular prism is directly proportional to the product of its dimensions (length, width, height). Changing any dimension affects the overall volume.

Front

How do you find the new volume of a rectangular prism when one dimension is changed?

Back

To find the new volume, multiply the new dimension by the unchanged dimensions and apply the volume formula: Volume = length × width × height.

Front

What is the effect of a scale factor of 4 on the dimensions and volume of a rectangular prism?

Back

A scale factor of 4 means each dimension is multiplied by 4, and the volume increases by a factor of 4^3 (64), making the new volume 64 times the original volume.

Front

If a rectangular prism has a volume of 220 cubic inches and the length is changed to achieve a volume of 440 cubic inches, what is the new length?

Back

The new length is 8 inches, as the volume doubled, indicating the length must also double.