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How is the volume of a shape affected by an enlargement of a scale factor of 2 and why?
When a shape is enlarged by a scale factor of 2, its volume is affected by a scale factor of 2 cubed, which is 8. This is because volume is a three-dimensional measurement, so each dimension (length, width, and height) is doubled. Therefore, the volume is multiplied by 2 x 2 x 2, resulting in an eightfold increase.
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What type of dilation occurs with a scale factor of 14?
The type of dilation that occurs with a scale factor of 14 is enlargement. Any time the scale factor is larger than 1, it is enlargement.
Another name for scale?
Enlargement factor.
How do you calculate enlargement of a cube?
To calculate the enlargement of a cube, you first determine the scale factor by which the cube's dimensions are increased. If the original side length is ( s ) and the new side length after enlargement is ( s' ), the scale factor ( k ) is given by ( k = \frac{s'}{s} ). The volume of the original cube is ( V = s^3 ), and the volume of the enlarged cube is ( V' = (s')^3 ), which can also be expressed as ( V' = k^3 \times V ). Thus, the volume increase can be determined by cubing the scale factor.
What information do you need to complete a given shape enlargement?
The scale or enlargement factor.
How can you determine whether a dilation's is a reduction or a enlargement?
To determine whether a dilation is a reduction or an enlargement, compare the scale factor to 1. If the scale factor is greater than 1, the dilation is an enlargement, as the image will be larger than the original. Conversely, if the scale factor is between 0 and 1, the dilation is a reduction, resulting in a smaller image. Additionally, you can observe the distances from the center of dilation; if they increase, it's an enlargement, and if they decrease, it's a reduction.
What type of dilation occurs with a scale factor of 14?
The type of dilation that occurs with a scale factor of 14 is enlargement. Any time the scale factor is larger than 1, it is enlargement.
What is a negative scale factor?
A negative scale factor is used to produce the image on the other side of the centre of enlargement (scaled to the absolute value of the scale factor).
Another name for scale?
Enlargement factor.
How do you calculate enlargement of a cube?
To calculate the enlargement of a cube, you first determine the scale factor by which the cube's dimensions are increased. If the original side length is ( s ) and the new side length after enlargement is ( s' ), the scale factor ( k ) is given by ( k = \frac{s'}{s} ). The volume of the original cube is ( V = s^3 ), and the volume of the enlarged cube is ( V' = (s')^3 ), which can also be expressed as ( V' = k^3 \times V ). Thus, the volume increase can be determined by cubing the scale factor.
What information do you need to complete a given shape enlargement?
The scale or enlargement factor.
What is an enlargement with a negative scale factor?
It is a smaller shape on the other side of the centre of enlargement.
A dilation is an enlargement if the scale factor is?
greater then 1
What happens to an enlarged image when the scale factor of enlargement is one?
Absolutely nothing. A scale factor of 1 is the same as saying do not change the scale.
If someone enlarged a drawing by a scale factor of 3 and got 396 cm squared what was the original drawing?
The scale factor is usually stated as a linear enlargement factor. Therefore, the area enlargement factor is the square of the scale factor, in this instance, 9. The area of the original drawing was thus 396/9 = 44 cm2.
How can you determine whether a dilation's is a reduction or a enlargement?
To determine whether a dilation is a reduction or an enlargement, compare the scale factor to 1. If the scale factor is greater than 1, the dilation is an enlargement, as the image will be larger than the original. Conversely, if the scale factor is between 0 and 1, the dilation is a reduction, resulting in a smaller image. Additionally, you can observe the distances from the center of dilation; if they increase, it's an enlargement, and if they decrease, it's a reduction.
Is a transformation that turns a figure to a fixed point?
An enlargement with a scale factor of 0.
What kind of scale factor produces an enlargement?
Scale factors whose absolute values are greater than 1.
