Question

Geometry 12.5 question 18

describe how the change affects the volume of the pyramid or cone. (See Examples 4 and 5.) 18. multiplying all the linear dimensions by 1/4

Answer 1

Multiplying all linear dimensions of a pyramid or cone by 1/4 reduces each dimension to a quarter of its size, resulting in a new volume that is 1/64th of the original volume since volume scales with the cube of the linear dimensions.

Step-by-step explanation:

When multiplying all linear dimensions of a pyramid or a cone by 1/4, you are effectively reducing each dimension to a quarter of its original size. The volume of a pyramid or a cone can be calculated using the formula V = 1/3 * base area * height. Since volume is a measure of three-dimensional space, when you scale down every linear dimension by a factor of 1/4, the new volume will be (1/4)³ of the original volume, because volume scales with the cube of the linear dimensions. This means the new volume is 1/64th the size of the original volume.