Question

A triangular pyramid with a volume of 96 in3 is dilated with a scale factor of k = 1.75. What is the new volume?

Answer 1

After a dilatation with a scale factor of 1.75, the new volume of a triangular pyramid originally with a volume of 96 in³ will increase to 514.5 in³.

Step-by-step explanation:

To find the new volume of a triangular pyramid after dilation, we can use the properties of scale factors in three dimensions. The volume of a three-dimensional figure after dilation with a scale factor k will be k³ times the original volume. In this case, the original volume is 96 in³ and the scale factor is 1.75. The new volume V' is calculated as follows:

V' = k³ * V

V' = 1.75³ * 96 in³

V' = 5.359375 * 96 in³

V' = 514.5 in³

Thus, the new volume after the dilatation is 514.5 in³.